some remarks about stochastic controllability for linear composite systems sufficient conditions of e controllability for a class of continuous parameter stochastic linear composite systems are established in this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure an example is given to illustrate the criterion

a separation principle for the h2 control of continuous time infinite markov jump linear systems with partial observations abstract in this paper we devise a separation principle for the h 2 optimal control problem of continuous time markov jump linear systems with partial observations and the markov process taking values in an infinite countable set s we consider that only an output and the jump parameters are available to the controller it is desired to design a dynamic markov jump controller such that the closed loop system is stochastically stable and minimizes the h 2 norm of the system as in the case with no jumps we show that an optimal controller can be obtained from two sets of infinite coupled algebraic riccati equations one associated with the optimal control problem when the state variable is available and the other one associated with the optimal filtering problem an important feature of our approach not previously found in the literature is to introduce an adjoint operator of the continuous time markov jump linear system to derive our results

robust stabilization for uncertain markovian jump fuzzy systems based on free weighting matrix method this paper presents a new methodology of robust state feedback fuzzy controller based on free weighting matrix method for a class of uncertain markovian jump nonlinear systems the class of systems under consideration is represented by the t s fuzzy model with partly known transition probability matrix the free weighting matrix method is proposed to obtain a less conservative stochastic stability criterion of the uncertain markovian jump fuzzy systems mjfss in terms of linear matrix inequalities lmis furthermore a sufficient condition for the mode dependent state feedback fuzzy controller is derived for the mjfss for all admissible parameter uncertainties finally a simulation example is provided to illustrate the effectiveness of the proposed methodology

a geometric method for detecting chaotic dynamics a new method of detection of chaos in dynamical systems generated by time periodic nonautonomous differential equations is presented it is based on the existence of some sets called periodic isolating segments in the extended phase space satisfying some topological conditions by chaos we mean the existence of a compact invariant set such that the poincare map is semiconjugated to the shift on two symbols and the counterimage by the semiconjugacy of any periodic point in the shift contains a periodic point of the poincare map as an application we prove that the planar equationz 1 ei t z 2 zgenerates chaotic dynamics provided 0 1 288

solution and asymptotic behavior of coupled riccati equations in jump linear systems a new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled riccati equations occurring in jump linear systems is derived by verifying a riccati inequality it is shown that such a solution exists in addition two numerical algorithms are given to compute it an example is given to illustrate the proposed method

a new perspective on the robustness of markov jump linear systems this paper is concerned with the robust analysis and control of continuous time markov jump linear systems the centerpiece of the paper is an alternative to the small gain theorem which hinges on the robustification of a certain adjoint lyapunov operator by means of this technique it is proven that the small gain theorem of markov jump linear systems may sometimes be arbitrarily conservative even when nonlinear lipschitz disturbances are taken into account the adjoint approach on the other hand provides the maximal degree of robustness for this particular setup in addition we prove that the adjoint design of controllers is solved more efficiently than the design based on small gain analysis bearing these new facts in mind we derive an iterative algorithm for the design of robust controllers based on linear matrix inequalities by means of numerical examples regarding the robust control of an underactuated manipulator arm and of a simplified power systems model it is shown that the adjoint design methodology can be much more advantageous than its small gain counterpart

stability of hybrid stochastic delay systems whose discrete components have a large state space a two time scale approach abstract this work is concerned with stability of stochastic differential delay equations with markovian switching where the modulating markov chain has a large state space and is subject to both fast and slow movements under simple conditions we demonstrate that if the limit systems are p th moment exponentially stable then the original systems are p th moment exponentially stable in an appropriate sense in addition the exponential stability is also investigated moreover stability in distribution is obtained for such hybrid systems

uniqueness of constrained viscosity solutions in hybrid control systems we study constrained viscosity solutions with an unbounded growth for a class of first order hamilton jacobi bellman equations arising in hybrid control systems to deal with the boundary constraint and rapid growth of the solutions we construct a particular set of test functions and under very mild conditions establish a comparison theorem which gives the estimate of distance between the subsolution and the supersolution the comparison theorem implies uniqueness of the constrained viscosity solution if its existence is ensured and under some additional assumptions we give an existence result by showing that the value function is a constrained viscosity solution we then apply the obtained uniqueness results to an optimal scheduling problem and finally to stochastic manufacturing systems

reduced order filtering for networks with markovian jumping parameters and missing measurements abstractthe problem of reduced order h filters design for markovian jumping complex networks with polytopic time varying transition probability matrices is first addressed in this paper where th

perturbation of multivariable linear quadratic systems with jump parameters considers the problem of the perturbation of a class of linear quadratic systems where the change from one structure for the dynamics and costs to another is governed by a finite state markov process the problem above leads to the analysis of some perturbed linearly coupled sets of riccati equations we show that the matrix obtained as the solution of the equations which determines the optimal value and control has a taylor expansion in the perturbation parameter we compute explicitly the terms of this expansion

stochastic stability and stabilization conditions of semi markovian jump systems with mode transition dependent sojourn time distributions this paper is concerned with the stochastic stability and stabilization problem for a class of continuous time semi markovian jump systems s mjss with mode transition dependent sojourn time distributions in contrast to other approaches this paper offers the possibility to explore more refined probability models on the sojourn time by considering the mode transition dependent sojourn time distributions instead of mode dependent ones here to construct a finite set of linear matrix inequalities lmis from sojourn time dependent matrix inequalities a less conservative relaxation method is proposed in such a way that all available constraints on time varying transition rates can be exploited simulation examples report the effectiveness of the proposed method

on the euclidean distance of images we present a new euclidean distance for images which we call image euclidean distance imed unlike the traditional euclidean distance imed takes into account the spatial relationships of pixels therefore it is robust to small perturbation of images we argue that imed is the only intuitively reasonable euclidean distance for images imed is then applied to image recognition the key advantage of this distance measure is that it can be embedded in most image classification techniques such as svm lda and pca the embedding is rather efficient by involving a transformation referred to as standardizing transform st we show that st is a transform domain smoothing using the face recognition technology feret database and two state of the art face identification algorithms we demonstrate a consistent performance improvement of the algorithms embedded with the new metric over their original versions

technical communique robust h2 control of continuous time markov jump linear systems this paper is concerned with the problem of designing robust h 2 state feedback controllers for continuous time markov jump linear systems subject to polytopic type parameter uncertainty based on the parameter dependent lyapunov function approach a new method for designing robust h 2 controllers is presented in terms of solutions to a set of linear matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed design method

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

convergence of gradient based iterative solution of coupled markovian jump lyapunov equations the solution of coupled discrete time markovian jump lyapunov matrix equations cdmjlmes is important in stability analysis and controller design for markovian jump linear systems this paper presents a simple and effective iterative method to produce numerical solutions to this class of matrix equations the gradient based algorithm is developed from an optimization point of view a necessary and sufficient condition guaranteeing the convergence of the algorithm is established this condition shows that the algorithm always converges provided the cdmjlmes have unique solutions which is evidently different from the existing results that converge conditionally a simple sufficient condition which is easy to test is also provided the optimal step size in the algorithm such that the convergence rate of the algorithm is maximized is given explicitly it turns out that an upper bound of the convergence rate is bounded by a function of the condition number of the augmented coefficient matrix of the cdmjlmes some parameters are introduced to the algorithm that will potentially reduce the condition number and thus increase the convergence rate of the algorithm a numerical example is used to illustrate the efficiency of the proposed approach

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

implicit iterative algorithms for continuous markovian jump lyapunov equations in this technical note implicit iterative algorithms with some tunable parameters are developed to solve the coupled lyapunov matrix equations associated with continuous time markovian jump linear systems a significant feature of the proposed algorithms is that the iterative sequences are updated by using not only the information in the last step but also the information in the current step and the previous steps also the convergence rate of the proposed algorithms can be significantly improved by choosing appropriate parameters in the algorithms

stabilization of continuous time jump linear systems we investigate almost sure and moment stabilization of continuous time jump linear systems with a finite state markov jump form process we first clarify the concepts of spl delta moment stabilizability exponential spl delta moment stabilizability and stochastic spl delta moment stabilizability we then present results on the relationships among these concepts coupled riccati equations that provide necessary and sufficient conditions for mean square stabilization are given in detail and an algorithm for solving the coupled riccati equations is proposed moreover we show that individual mode controllability implies almost sure stabilizability which is not true for other types of stabilizability finally we present some testable sufficient conditions for spl delta moment stabilizability and almost sure stabilizability

brief continuous time state feedback h2 control of markovian jump linear systems via convex analysis continuous time h 2 control problem for the class of linear systems with markovian jumps mjls using convex analysis is considered in this paper the definition of the h 2 norm for continuous time mjls is presented and related to the appropriate observability and controllability gramians a convex programming formulation for the h 2 control problem of mjls is developed that enables us to tackle the optimization problem of mjls under the assumption that the transition rate matrix p p i j for the markov chain may not be exactly known but belongs to an appropriate convex set an equivalence between the convex formulation when p is exactly known and the usual dynamic programming approach of quadratic optimal control of mjls is established it is shown that there exists a solution for the convex programming problem if and only if there exists the mean square stabilizing solution for a set of coupled algebraic riccati equations these results are compared with other related works in the current literature

lyapunov iterations for optimal control of jump linear systems at steady state in this paper we construct a sequence of lyapunov algebraic equations whose solutions converge to the solutions of the coupled algebraic riccati equations of the optimal control problem for jump linear systems the obtained solutions are positive semidefinite stabilizing and unique the proposed algorithm is extremely efficient from the numerical point of view since it operates only on the reduced order decoupled lyapunov equations several examples are included to demonstrate the procedure

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

a convex programming approach to h2 control of discrete time markovian jump linear systems in this paper we consider the h control problem for the class of discrete time 2 linear systems with parameters subject to markovian jumps using a convex programming approach we generalize the definition of the h norm from the deter2 ministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians conditions for existence and derivation of a mean square stabilizing controller for a markovian jump linear system using convex analysis are established the main contribution of the paper is to provide a convex programming formulation to the h control problem so that several 2 important cases to our knowledge not analysed in previous work can be addressed regarding the transition matrix p for the markov chain two ij situations are considered the case in which it is exactly known and the case in which it is not exactly known but belongs to an appropriated convex set regarding the state variable and the jump variable the cases in which t

classification of hyperspectral images by tensor modeling and additive morphological decomposition pixel wise classification in high dimensional multivariate images is investigated the proposed method deals with the joint use of spectral and spatial information provided in hyperspectral images additive morphological decomposition amd based on morphological operators is proposed amd defines a scale space decomposition for multivariate images without any loss of information amd is modeled as a tensor structure and tensor principal components analysis is compared as dimensional reduction algorithm versus classic approach experimental comparison shows that the proposed algorithm can provide better performance for the pixel classification of hyperspectral image than many other well known techniques highlights additive morphological decomposition without any loss of information is proposed decomposition is modeled as a tensor structure tensor pca is compared versus pca proposed workflow performs better than other techniques in hsi classification

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

observation for markov jump piecewise affine systems with admissible region switching paths the technical note investigates the problem of state observation for discrete time markov jump piecewise affine pwa systems which cover both markov jump systems and traditional pwa systems as two special classes a new method for determining the admissible region switching paths between adjacent time instants is proposed for both the plant state and the estimator state so that both the computation cost and the conservatism of the theoretical results are reduced to analyze the mean square stability of the observation error system a novel piecewise lyapunov function is constructed which depends on the current mode and the region indices of both the system and observer states as the partitions of the state space are different for different modes the region indices are dependent on the system mode then mode dependent pwa observers are designed by means of s procedure and ellipsoidal outer approximation such that the observation error system is mean square stable the proposed observation strategy is demonstrated via an illustrative example

h2 optimal control for linear stochastic systems the aim of the present paper is to provide an optimal solution to the h 2 state feedback and output feedback control problems for stochastic linear systems subjected both to markov jumps and to multiplicative white noise it is proved that in the state feedback case the optimal solution is a static gain which is also optimal in the class of all higher order controllers in the output feedback case the optimal h 2 controller has the same order as the given stochastic system the realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of riccati type coupled equations an effective iterative convergent algorithm to compute these stabilizing solutions is also presented the paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature

optimal quadratic control of jump linear systems with separately controlled transition probabilities abstract the optimal control of discrete time jump systems that would be linear but for randomly jumping parameters are considered these parameter jumps which are indexed by a finite state form process can be used to model systems subject to component failures or structural changes the control of such systems when the jump probabilities can be controlled by choice of a finite valued input is considered this input form control can be thought of as corresponding to a maintenance or repair policy the optimal control problem with quadratic costs whose weighting matrices depend on the jumping parameters and form control is formulated for such systems the optimal solution for finite and infinite time horizon problems is developed in addition sufficient conditions for the existence of a steady state stabilizing solution to the infinite time problem are given in terms of appropriately defined controllability and observability properties

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

a note on stability of hybrid stochastic differential equations the method is different from those usual methods used in previous literature some harsh restrictions imposed on diffusion operators have been removed the differentiability of delays has been removed we studied the robustness of exponential stability respect to delays in this paper the pth moment stability of hybrid stochastic differential equations is investigated several new sufficient conditions are derived by constructing an auxiliary delayed differential equation and using the comparison principle the proposed criteria remove some harsh restrictions imposed on the diffusion operators and improve some previous related works numerical examples and simulations are given to illustrate the effectiveness of theoretical results

max min distance analysis by using sequential sdp relaxation for dimension reduction we propose a new criterion for discriminative dimension reduction max min distance analysis mmda given a data set with c classes represented by homoscedastic gaussians mmda maximizes the minimum pairwise distance of these c classes in the selected low dimensional subspace thus unlike fisher s linear discriminant analysis flda and other popular discriminative dimension reduction criteria mmda duly considers the separation of all class pairs to deal with general case of data distribution we also extend mmda to kernel mmda kmmda dimension reduction via mmda kmmda leads to a nonsmooth max min optimization problem with orthonormal constraints we develop a sequential convex relaxation algorithm to solve it approximately to evaluate the effectiveness of the proposed criterion and the corresponding algorithm we conduct classification and data visualization experiments on both synthetic data and real data sets experimental results demonstrate the effectiveness of mmda kmmda associated with the proposed optimization algorithm

a survey of multilinear subspace learning for tensor data increasingly large amount of multidimensional data are being generated on a daily basis in many applications this leads to a strong demand for learning algorithms to extract useful information from these massive data this paper surveys the field of multilinear subspace learning msl for dimensionality reduction of multidimensional data directly from their tensorial representations it discusses the central issues of msl including establishing the foundations of the field via multilinear projections formulating a unifying msl framework for systematic treatment of the problem examining the algorithmic aspects of typical msl solutions and categorizing both unsupervised and supervised msl algorithms into taxonomies lastly the paper summarizes a wide range of msl applications and concludes with perspectives on future research directions

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

discovering diverse subset for unsupervised hyperspectral band selection band selection as a special case of the feature selection problem tries to remove redundant bands and select a few important bands to represent the whole image cube this has attracted much attention since the selected bands provide discriminative information for further applications and reduce the computational burden though hyperspectral band selection has gained rapid development in recent years it is still a challenging task because of the following requirements 1 an effective model can capture the underlying relations between different high dimensional spectral bands 2 a fast and robust measure function can adapt to general hyperspectral tasks and 3 an efficient search strategy can find the desired selected bands in reasonable computational time to satisfy these requirements a multigraph determinantal point process mdpp model is proposed to capture the full structure between different bands and efficiently find the optimal band subset in extensive hyperspectral applications there are three main contributions 1 graphical model is naturally transferred to address band selection problem by the proposed mdpp 2 multiple graphs are designed to capture the intrinsic relationships between hyperspectral bands and 3 mixture dpp is proposed to model the multiple dependencies in the proposed multiple graphs and offers an efficient search strategy to select the optimal bands to verify the superiority of the proposed method experiments have been conducted on three hyperspectral applications such as hyperspectral classification anomaly detection and target detection the reliability of the proposed method in generic hyperspectral tasks is experimentally proved on four real world hyperspectral data sets

stochastic stabilization of a class of nonhomogeneous markovian jump linear systems this paper deals with the problem of stochastic stability analysis and control synthesis of a class of markovian jump linear systems mjls with time varying transition probabilities tps in the discrete time domain the time varying character is considered to be in a polytopic sense the approach followed in this note is based on the use of a parameter dependent stochastic lyapunov function we give a stability condition in terms of a linear matrix inequality lmi feasibility problem the obtained results are illustrated in a numerical example

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

practical stability controllability and optimal control of stochastic markovian jump systems with time delays the notions of the practical stability in probability and in the pth mean and the practical controllability in probability and in the pth mean are introduced for some stochastic systems with markovian jump parameters and time varying delays sufficient conditions on such practical properties are obtained by using the comparison principle and the lyapunov function methods besides for a class of stochastic nonlinear systems with markovian jump parameters and time varying delays existence conditions of optimal control are discussed particularly for linear systems optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

controllability of stochastic linear systems in the paper necessary and sufficient conditions for various types of stochastic controllability of the linear stochastic system of the form d x ax d t bu d t c d w r x 0 x 0 are given some possible extensions are indicated as well

output feedback for a class of linear systems with stochastic jump parameters a class of linear systems subject to sudden jumps in parameter values is studied for a quadratic performance index the optimal controller has already been proposed it consists of a full state feedback that requires the synthesis of an observer for the plant state and mode to avoid this difficulty the present note develops new results that lead to the selection of the best feedback control law depending only on measurable outputs necessary optimality conditions are derived and two computationnal algorithms proposed an example is included

local coordinates alignment with global preservation for dimensionality reduction dimensionality reduction is vital in many fields and alignment based methods for nonlinear dimensionality reduction have become popular recently because they can map the high dimensional data into a low dimensional subspace with the property of local isometry however the relationships between patches in original high dimensional space cannot be ensured to be fully preserved during the alignment process in this paper we propose a novel method for nonlinear dimensionality reduction called local coordinates alignment with global preservation we first introduce a reasonable definition of topology preserving landmarks tpls which not only contribute to preserving the global structure of datasets and constructing a collection of overlapping linear patches but they also ensure that the right landmark is allocated to the new test point then an existing method for dimensionality reduction that has good performance in preserving the global structure is used to derive the low dimensional coordinates of tpls local coordinates of each patch are derived using tangent space of the manifold at the corresponding landmark and then these local coordinates are aligned into a global coordinate space with the set of landmarks in low dimensional space as reference points the proposed alignment method called landmarks based alignment can produce a closed form solution without any constraints while most previous alignment based methods impose the unit covariance constraint which will result in the deficiency of global metrics and undesired rescaling of the manifold experiments on both synthetic and real world datasets demonstrate the effectiveness of the proposed algorithm

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic riccati equation this note addresses the jump linear quadratic problem of markov jump linear systems and the associated algebraic riccati equation necessary and sufficient conditions for stability of the optimal control and positiveness of riccati solutions are developed we show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stability of the associated trajectory but also a necessary one this together with a characterization developed here for the kernel of the riccati solution allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable and that the riccati solution is positive definite if and only if the system is weakly observable the connection between the algebraic riccati equation and the control problem is made as far as the minimal positive semidefinite solution for the algebraic riccati equation is identified with the optimal solution of the linear quadratic problem illustrative numerical examples and comparisons are included

event triggered communication for synchronization of markovian jump delayed complex networks with partially unknown transition rates the network model in this paper involves time delay and partly unknown transition rates which is more practical than the models in 18 34 35 38 different from the most existing results with partly unknown transition rates 24 26 the synchronization trajectory in this paper is dynamic which will be adjusted according to the states of nodes a randomly occurring event triggered control strategy is proposed to study the synchronization issue of markovian jump delayed complex networks with partly unknown transition rates the positive lower bound of the event intervals is obtained which can exclude undesired accumulation of event instants zeno behaviors in this paper exponential synchronization problems are investigated for an array of markovian jump delayed complex networks with partially unknown transition rates and discontinuous diffusions to impel the array complex networks to achieve exponential synchronization a new randomly occurring event triggered control strategy is proposed the idea of event triggered control strategy is that the coupling term and controller update data only at the event triggered instants which can reduce the communication load and energy consumption by constructing a novel stochastic lyapunov krasovskii function some exponential synchronization criteria are obtained in terms of lmis and famous halanay inequality furthermore we obtain a positive lower bound of the event intervals which can exclude the zeno behaviors finally a simulation example is given to illustrate the effectiveness of the theoretical results

robust jump linear quadratic control a mode stabilizing solution this correspondence is concerned with optimal feedback control of a class of linear stochastic systems for a quadratic performance index the solution to this problem is known but the resulting optimal regulator does not ensure stability in every mode of operation to improve robustness a new mode stabilizing solution is defined an example illustrates the advantages of the proposed controller

stability of discrete time linear systems with markovian jumping parameters and constrained control the note is devoted to the study of linear discrete time systems with markovian jumping parameters and constrained control the constraints used in the note are of symmetrical inequality type the approach of positively invariant sets is used to obtain new necessary and sufficient conditions for positive invariance and sufficient conditions for stochastic stability these conditions become those given for stationary discrete time systems with one mode deterministic linear discrete time systems as known in the literature

robust stability of a class of uncertain markov jump nonlinear systems this note addresses the problem of robust stability analysis for a class of markov jump nonlinear systems subject to polytopic type parameter uncertainty a condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed an estimate of a robust domain of attraction of the origin is also provided the approach is based on a stochastic lyapunov function with polynomial dependence on the system state and uncertain parameters a numerical example illustrates the proposed result

a constructive method to static output stabilisation of markov jump systems this paper is concerned with the static output feedback stabilisation of markov jump systems transition probabilities are assumed to be incomplete namely they may be known uncertain with known lower and upper bounds and unknown to linearise the nonlinearities induced by unknown transition probabilities a linearisation is developed to solve the static output feedback problem by means of linear matrix inequalities a constructive method is proposed to separate the controller gain matrices from lyapunov variables based on the linearisation and the separation sufficient conditions are established to guarantee that the closed loop system is stochastically stable by the designed static output feedback controller the obtained results are further extended to deal with norm bounded or polytopic uncertainties on system matrices numerical examples are given to demonstrate the effectiveness of the proposed method

hybrid dimensionality reduction method based on support vector machine and independent component analysis this paper presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk supervised criterion and data independence unsupervised criterion classification accuracy is used as a metric to evaluate the performance of the method by minimizing the structural risk projection originated from the decision boundaries directly improves the classification performance from a supervised perspective from an unsupervised perspective projection can also be obtained based on maximum independence among features or attributes in data to indirectly achieve better classification accuracy over more intrinsic representation of the data orthogonality interrelates the two sets of projections such that minimum redundancy exists between the projections leading to more effective dimensionality reduction experimental results show that the proposed hybrid dimensionality reduction method that satisfies both criteria simultaneously provides higher classification performance especially for noisy data sets in relatively lower dimensional space than various existing methods

optimal time weighted h 2 model reduction for markovian jump systems this article addresses the optimal time weighted h 2 model reduction problem for markovian jump linear systems that is for a given mean square stable markovian jump system our aim is to find a mean square stable jump system of lower order such that the time weighted h 2 norm of the corresponding error system is minimised the time weighted h 2 norm of the system is first defined and then a computational method is constructed the computation requires the solution of two sets of recursive lyapunov type linear matrix equations associated with the markovian jump system to solve the optimal time weighted h 2 model reduction problem we propose a gradient flow method for its solution a necessary condition for minimality is derived and a computational procedure is provided to obtain the minimising reduced order model the necessary condition generalises the standard result for systems when markov jumps and the time weighting term do not appear finally two numerical examples are given to demonstrate the

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

stability analysis and stabilization of discrete time non homogeneous semi markov jump linear systems a polytopic approach abstract this paper addresses the issues of stability analysis and stabilizing controller design for two classes of discrete time non homogeneous semi markov jump linear systems s mjlss the first class is concerned with the sojourn time probability mass functions that are independent of jump instants while the other considers the existence of probability mass functions of sojourn time depending on jump instants new techniques are developed respectively for both classes of systems by transforming their corresponding time varying semi markov kernels into more tractable forms based on the stochastic stability allowing for bounded sojourn time the derived stability and stabilization criteria containing the probability distribution information of random sojourn time can be numerically tested in order to reduce the possible conservatism of the obtained results a novel class of polytopic quadratic lyapunov function is constructed which depends on both the current mode and the elapsed time in the current mode finally the proposed control strategies are applied to an illustrative application of automotive electronic throttle valve to show the effectiveness of the theoretical results the results also reveal the significance of considering the inhomogeneity of s mjlss and the importance of our constructed lyapunov function

an implicit sequential algorithm for solving coupled lyapunov equations of continuous time markovian jump systems in this paper an implicit sequential algorithm is presented for solving coupled lyapunov matrix equations of continuous time markovian jump linear systems first some existing iterative algorithms which can be utilized to solve the coupled lyapunov matrix equations are reviewed and discussed next based on the existing parallel iterative algorithm an implicit sequential algorithm is proposed by using the latest updated information the proposed algorithm fills the current gap of implicit algorithms for solving continuous coupled lyapunov matrix equations it is shown that the proposed algorithm with zero initial conditions can monotonically converge to the unique positive definite solutions of the coupled lyapunov matrix equations if the associated markovian jump system is stochastically stable moreover a necessary and sufficient condition is established for the proposed algorithm to be convergent the algorithm presented in this paper has much better convergence performance than other existing iterative algorithms and requires less storage capacity finally a numerical example is given to show the effectiveness of the proposed algorithm

h 2 control of discrete time periodic systems with markovian jumps and multiplicative noise this paper addresses the problem of optimal and robust h2 control for discrete time periodic systems with markov jump parameters and multiplicative noise to analyse the system performance in the presence of exogenous random disturbance an h2 norm is firstly established on the basis of gramian matrices further under the condition of exact observability a necessary and sufficient condition is presented for the solvability of h2 optimal control problem by means of a generalised riccati equation when the transition probabilities of jump parameter are incompletely measurable an h2 guaranteed cost norm is exploited and the robust h2 controller is designed through a linear matrix inequality lmi optimisation approach an example of a networked control system is supplied to illustrate the proposed results

bilinear probabilistic principal component analysis probabilistic principal component analysis ppca is a popular linear latent variable model for performing dimension reduction on 1 d data in a probabilistic manner however when used on 2 d data such as images ppca suffers from the curse of dimensionality due to the subsequently large number of model parameters to overcome this problem we propose in this paper a novel probabilistic model on 2 d data called bilinear ppca bppca this allows the establishment of a closer tie between bppca and its nonprobabilistic counterpart moreover two efficient parameter estimation algorithms for fitting bppca are also developed experiments on a number of 2 d synthetic and real world data sets show that bppca is more accurate than existing probabilistic and nonprobabilistic dimension reduction methods

robust stability and boundedness of nonlinear hybrid stochastic differential delay equations one of the important issues in the study of hybrid stochastic differential delay equations sddes is the automatic control with consequent emphasis being placed on the asymptotic analysis of stability and boundedness in the study of asymptotic properties the robust stability has received a great deal of attention the theory of robust stability shows how much perturbation a given stable hybrid sdde can tolerate so that its perturbed system remains stable almost all results so far on the robust stability require that the underlying sddes be either linear or nonlinear with linear growth condition however little is known on the robust stability of nonlinear hybrid sddes without the linear growth condition which is one of the key topics in this paper the other key topic is the robust boundedness the aim here is to answer the question how much perturbation can a given asymptotically bounded hybrid sdde tolerate so that its perturbed system remains asymptotically bounded

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

periodic solutions of complex valued differential equations and systems with periodic coefficients has been considered by srzednicki 11 13 using a combination of generalized conley s isolating blocks the index of singular points of autonomous systems and the lefschetz fixed point theorem recently it has been shown that slight extensions of srzednicki s results could be obtained in a simpler and more elementary way using continuation theorems of the leray schauder type see 6 9 the aim of the present paper is to show that the same methodology can be adapted to prove the existence of periodic solutions for more general classes of equations and systems article no 0054

tensor distance based multilinear locality preserved maximum information embedding this brief paper presents a unified framework for tensor based dimensionality reduction dr with a new tensor distance td metric and a novel multilinear locality preserved maximum information embedding mlpmie algorithm different from traditional euclidean distance which is constrained by the orthogonality assumption td measures the distance between data points by considering the relationships among different coordinates to preserve the natural tensor structure in low dimensional space mlpmie directly works on the high order form of input data and iteratively learns the transformation matrices in order to preserve the local geometry and to maximize the global discrimination simultaneously mlpmie keeps both local and global structures in a manifold model by integrating td into tensor embedding td mlpmie performs tensor based dr through the whole learning procedure and achieves stable performance improvement on various standard datasets

on the iterative refinement of matrix upper bounds for the solution of continuous coupled algebraic riccati equations abstract in this paper we develop a new approach for the iterative refinement algorithm along with fully mathematical justifications which sharpens matrix solution upper bounds for the well known continuous coupled algebraic riccati equation ccare our methodology is studied within a broader framework recently proposed in xu in press several desirable properties of the algorithm are then established which include the strict monotonicity and convergence of the sequences generated by the algorithm thus strengthening the existing results in the literature for computing tighter matrix upper solution bounds for the ccare in addition new admissibility conditions within the general framework are proposed which guarantee tighter matrix upper solution bounds to be computed from the algorithm

comments on robust jump linear quadratic control a mode stabilizing solution in the above paper an optimal control problem with discounting was proposed to achieve closed loop mode stabilization for linear systems with jump parameters the paper used the unstated hypothesis that the diagonal entries of the generator of the jump process are equal this correspondence discusses the situation in the general case

almost sure and moments stability of jump linear systems abstract the stability of piecewise deterministic linear systems driven by an underlying finite markov chain is analyzed necessary and sufficient conditions for moment stability are obtained by means of an explicit formula for the corresponding liapunov exponent the relationship between almost sure and moment stability is elucidated revealing the possible occurrence of high order moment instability and large deviations from a stable sample path behavior

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

controllability of linear stochastic systems abstract we discuss several concepts of controllability for stochastic systems and derive sufficient and in most cases also necessary algebraic conditions for the controllability of the state and the output of white and colored noise linear systems these criteria reduce to the well known deterministic ones in the absence of noise

on controlability of linear systems with stochastic jump parameters this note studies the notion of stochastic e controllability in probability for linear systems subject to sudden jumps in parameter values by using a lyapunov like approach sufficient conditions are obtained in terms of a set of coupled bernoulli equations the potential use of the results is illustrated by an example

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

improved fuzzy control design for nonlinear markovian jump systems with incomplete transition descriptions this paper addresses the state feedback control of nonlinear continuous time markovian jump systems the nonlinearity is represented by takagi sugeno fuzzy models and the transition probability matrix is assumed to be partly known some elements in the matrix are known some are unknown but with known lower and upper bounds and some are completely unknown by making full use of the continuous property of the transition probability matrix new sufficient conditions for the stochastic stability of the system are obtained in terms of linear matrix inequalities we show that the conditions given are less conservative than or at least the same as those for existing results moreover using the conditions obtained we establish a method for design of a h state feedback controller numerical examples illustrate the effectiveness of the proposed method

almost sure stabilization of uncertain continuous time markov jump linear systems this work deals with the robust almost sure as stabilization problem for continuous time markov jump linear systems mjls norm bounded uncertainties affecting the system state and input matrices are considered a deterministically testable sufficient condition for robust as stability is provided which relies on a bound on the 2 norm of the system transition matrix such a condition can be profitably employed also to design a robust feedback stabilization strategy such feedback design is based on a formulation of the sufficient condition for robust as stability in terms of an equivalent lmi problem

brief paper stochastically exponential stability and stabilization of uncertain linear hyperbolic pde systems with markov jumping parameters this paper is concerned with the problem of robustly stochastically exponential stability and stabilization for a class of distributed parameter systems described by uncertain linear first order hyperbolic partial differential equations fohpdes with markov jumping parameters for which the manipulated input is distributed in space based on an integral type stochastic lyapunov functional islf the sufficient condition of robustly stochastically exponential stability with a given decay rate is first derived in terms of spatial differential linear matrix inequalities sdlmis then an sdlmi approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition furthermore using the finite difference method and the standard linear matrix inequality lmi optimization techniques recursive lmi algorithms for solving the sdlmis in the analysis and synthesis are provided finally a simulation example is given to demonstrate the effectiveness of the developed design method

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

remark on krasnosielski s guiding functions and srzednicki s periodic segments abstract we show that the existence of the complete set of guiding functions guarantees the existence of periodic isolating segment that carries the same information concerning periodic solutions of the non autonomous periodic equations x f x t

dimensionality reduction for hyperspectral data based on class aware tensor neighborhood graph and patch alignment to take full advantage of hyperspectral information to avoid data redundancy and to address the curse of dimensionality concern dimensionality reduction dr becomes particularly important to analyze hyperspectral data exploring the tensor characteristic of hyperspectral data a dr algorithm based on class aware tensor neighborhood graph and patch alignment is proposed here first hyperspectral data are represented in the tensor form through a window field to keep the spatial information of each pixel second using a tensor distance criterion a class aware tensor neighborhood graph containing discriminating information is obtained in the third step employing the patch alignment framework extended to the tensor space we can obtain global optimal spectral spatial information finally the solution of the tensor subspace is calculated using an iterative method and low dimensional projection matrixes for hyperspectral data are obtained accordingly the proposed method effectively explores the spectral and spatial information in hyperspectral data simultaneously experimental results on 3 real hyperspectral datasets show that compared with some popular vector and tensor based dr algorithms the proposed method can yield better performance with less tensor training samples required

multilinear discriminant analysis for face recognition there is a growing interest in subspace learning techniques for face recognition however the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma in this paper we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order first we propose a discriminant tensor criterion whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction then a novel approach called k mode optimization is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions we call this algorithm multilinear discriminant analysis mda which has the following characteristics 1 multiple interrelated subspaces can collaborate to discriminate different classes 2 for classification problems involving higher order tensors the mda algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem and 3 the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k mode optimization we provide extensive experiments on orl cmu pie and feret databases by encoding face images as second or third order tensors to demonstrate that the proposed mda algorithm based on higher order tensors has the potential to outperform the traditional vector based subspace learning algorithms especially in the cases with small sample sizes

stabilization of markovian systems via probability rate synthesis and output feedback this technical note is concerned with the stabilization problem of markovian jump linear systems via designing switching probability rate matrices and static output feedback gains a novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of markovian jump linear systems based on this a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices extensions to the polytopic uncertain case are also provided all the conditions are formulated in terms of linear matrix inequalities with some equality constraints which can be solved by two modified cone complementarity linearization algorithms examples are given to show the effectiveness of the proposed method

progressive dimensionality reduction by transform for hyperspectral imagery this paper develops to a new concept called progressive dimensionality reduction by transform pdrt which is particularly designed to perform data dimensionality reduction in terms of progressive information preservation in order to materialize the prdt a key issue is to prioritize information contained in each spectral transformed component so that all the spectral transformed components will be ranked in accordance with their information priorities in doing so projection pursuit pp based dimensionality reduction by transform drt techniques are developed for this purpose where the projection index pi is used to define the direction of interestingness of a pp transformed component referred to as projection index component pic the information contained in a pic is then calculated by the pi and used as the priority score of this particular pic such a resultant pdrt is called progressive dimensionality reduction by projection index based projection pursuit pdr pipp which performs pdrt by retaining an appropriate set of pics for information preservation according to their priorities two procedures are further developed to carry out pdr pipp in a forward or a backward manner referred to forward pdr pipp fpdr pipp or backward pdrt bpdr pipp respectively where fpdr pipp can be considered as progressive band expansion by starting with a minimum number of pics and adding new pics progressively according to their reduced priorities as opposed to bpdrt which can be regarded progressive band reduction by beginning with a maximum number of pics and removing pics with least priorities progressively both procedures are terminated when a stopping rule is satisfied the advantages of pdr pipp allow users to transmit communicate process and store data more efficiently and effectively in the sense of retaining data integrity progressively

mpca multilinear principal component analysis of tensor objects this paper introduces a multilinear principal component analysis mpca framework for tensor object feature extraction objects of interest in many computer vision and pattern recognition applications such as 2d 3d images and video sequences are naturally described as tensors or multilinear arrays the proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation the solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems as part of this work methods for subspace dimensionality determination are proposed and analyzed it is shown that the mpca framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis pca and its 2d variant 2d pca finally a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy and applied to the problem of gait recognition results presented here indicate mpca s utility as a feature extraction tool it is shown that even without a fully optimized design an mpca based gait recognition module achieves highly competitive performance and compares favorably to the state of the art gait recognizers