necessary and sufficient small gain conditions for integral input to state stable systems a lyapunov perspective this paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input to state stable iiss systems with external inputs the treatment of iiss and input to state stable iss systems is unified both necessary conditions and sufficient conditions are investigated using a lyapunov formulation in the presence of model uncertainty this paper proves that for the stability of the interconnected system at least one subsystem is necessarily iss which is a stronger stability property in the set of iiss the necessity of a small gain type property is also demonstrated this paper proposes a common form of smooth lyapunov functions which can establish the iiss and the iss of the interconnection comprising iiss and iss subsystems whenever the small gain type condition is satisfied the result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature global asymptotic stability is discussed as a special case

exponential stabilization of nonholonomic chained systems this paper presents a feedback control scheme for the stabilization of two input driftless chained nonholonomic systems also called chained form these systems are controllable but not asymptotically stabilizable by a smooth static state feedback control law in addition exponential stability cannot be obtained with a smooth time varying feedback control law here global asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth time varying feedback control law the control law depends in addition to the state and time on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state the inputs are differentiable with respect to time and tend exponentially toward zero for use in the analysis a lemma on the exponential convergence of a stable time varying nonlinear system perturbed by an exponentially decaying signal is presented simulation results are also shown

on subspace distances determined by the frobenius norm abstract two measures of separation between two subspaces of a finite dimensional complex vector space are introduced and investigated the measures were inspired by known expressions for the cosines of the angle and minimal angle between subspaces and are based on the frobenius norm by using partitioned representations of a pair of orthogonal projectors several properties of the measures are identified and their links with other notions used to characterize a separation between subspaces are pointed out

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

discrete time homogeneity robustness and approximation in this paper we study robustness properties of discrete time homogeneous systems we also analyse stability and robustness properties of a more general class of nonlin ear discrete time systems that can be approximated by homogeneous ones we apply the results to the investigation of stability properties of discretized continuous time systems

a method of illumination compensation for human face image based on quotient image illumination variation is one of the critical factors affecting face recognition rate a novel approach for human face illumination compensation is presented in this paper it constructs the nine dimension face illumination subspace based on quotient image in addition with the aim to improve algorithm efficiency a half face illumination image is proposed and the low dimension training set of the face image under different illumination conditions are obtained by means of pca and wavelet transform after processing two different illumination compensation strategies are given one is adding light and the other is removing light based on the illumination compensation strategy we implement the typical illumination sample image synthesis and the standard illumination sample image synthesis on a pca feature subspace and a wavelet transform subspace respectively and the illumination compensation of the gray images and the color images are further realized experimental results based on the yale face database b the extended yale face database b and the cas peal face database indicate that execution time after compensation is approximately half the time and face recognition rate is improved by 20 compared with that of the original images

multirate sampling and input to state stable receding horizon control for nonlinear systems abstract in this paper a robust receding horizon control for multirate sampled data nonlinear systems with bounded disturbances is presented the proposed receding horizon control is based on the solution of bolza type optimal control problems for the approximate discrete time model of the nominal system low measurement rate is assumed it is shown that the multistep receding horizon controller that stabilizes the nominal approximate discrete time model also practically input to state stabilizes the exact discrete time system with disturbances

on angles and distances between subspaces abstract the angles and distances between two given subspaces of c n 1 are investigated on the basis of a joint decomposition of the corresponding orthogonal projectors several new results are established with the particular attention paid to the notions of inclinedness and minimal angle to demonstrate the usefulness of the approach utilized some results known to be valid in hilbert space are reestablished in c n 1 either in generalized form or with considerably shorter proofs than in the original sources

input to state stability for discrete time time varying systems with applications to robust stabilization of systems in power form input to state stability iss of a parameterized family of discrete time time varying nonlinear systems is investigated a converse lyapunov theorem for such systems is developed we consider parameterized families of discrete time systems and concentrate on a semiglobal practical type of stability that naturally arises when an approximate discrete time model is used to design a controller for a sampled data system an application of our main result to time varying periodic systems is presented and this is used to solve a robust stabilization problem namely to design a control law for systems in power form yielding semiglobal practical iss sp iss

on disjoint range matrices abstract for a square complex matrix f and for f being its conjugate transpose the class of matrices satisfying r f r f 0 where r denotes range column space of a matrix argument is investigated besides identifying a number of its properties several functions of f such as f f f f ff f f and f f are considered particular attention is paid to the moore penrose inverses of those functions and projectors attributed to them it is shown that some results scattered in the literature whose complexity practically prevents them from being used to deal with real problems can be replaced with much simpler expressions when the ranges of f and f are disjoint furthermore as a by product of the derived formulae one obtains a variety of relevant facts concerning for instance rank and range

stability of discrete time delayed impulsive linear systems with application to multi tracking this paper studies the stability issue for discrete time delayed impulsive systems ddis the ddis model is formulated from a discrete time delayed system with impulses by using the matrix spectrum theory the estimates of solution with growth exponent are derived for delayed difference inequalities based on these results two types of criteria on exponential stability with an estimated convergence rate have been established for ddis the first type investigates the effect of destabilising impulses while the second is for the case in which the impulses stabilise the unstable discrete time delayed systems as the application the stability results are used to solve the multi tracking issue for discrete time dynamical networks by mixed impulsive networked control minc in which the impulsive control signals are transmitted via a communication network the effect of data dropout of impulsive control signals is also investigated and the maximal allowable dropout rate is estimated for the designed minc

controllability and observability for a class of controlled switching impulsive systems in this note we study the controllability and observability problem for a class of controlled switching impulsive systems by proposing several formula of variation of parameters for this type of time varying systems and employing the characteristic polynomial theory of matrix we establish necessary and sufficient conditions for controllability and controlled observability with respect to a given switching time sequence specializing the obtained results to the case of time invariant linear switching impulsive systems we derive some simple algebraic criteria which include the results reported in the literature for time invariant linear switching systems linear impulsive systems and classical linear systems one example is worked out for illustration

on uniform asymptotic stability of time varying parameterized discrete time cascades recently a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been proposed in the literature in this paper we develop novel tools that can be used within this framework and that are useful for tracking problems in particular results for stability analysis of parameterized time varying discrete time cascaded systems are given this class of models arises naturally when one uses an approximate discrete time model to design a stabilizing or tracking controller for a sampled data plant while some of our results parallel their continuous time counterparts the stability properties that are considered the conditions that are imposed and the the proof techniques that are used are tailored for approximate discrete time systems and are technically different from those in the continuous time context a result on constructing strict lyapunov functions from nonstrict ones that is of independent interest is also presented we illustrate the utility of our results in the case study of the tracking control of a mobile robot this application is fairly illustrative of the technical differences and obstacles encountered in the analysis of discrete time parameterized systems

rotation invariants of vector fields from orthogonal moments abstract vector field images are a type of new multidimensional data that appear in many engineering areas although the vector fields can be visualized as images they differ from graylevel and color images in several aspects to analyze them special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area in this paper we propose a method for the description and matching of vector field patterns under an unknown rotation of the field rotation of a vector field is so called total rotation where the action is applied not only on the spatial coordinates but also on the field values invariants of vector fields with respect to total rotation constructed from orthogonal gaussian hermite moments and zernike moments are introduced their numerical stability is shown to be better than that of the invariants published so far we demonstrate their usefulness in a real world template matching application of rotated vector fields

stability of solutions for stochastic impulsive systems via comparison approach this note studies stability problem of solutions for stochastic impulsive systems by employing lyapunov like function method and it s formula comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established based on these comparison principles the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system as the application the stability results are used to design impulsive control for the stabilization of unstable stochastic systems finally one example is given to illustrate the obtained results

robust stabilization of chained systems via hybrid control the problem of global robust exponential stabilization of nonholonomic chained systems is addressed and solved by means of a hybrid state feedback control law it is shown that the control law yields global exponential stability and global robustness against a class of small measurement errors actuator noises and exogenous disturbances

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

lyapunov formulation of the large scale iss cyclic small gain theorem the discrete time case abstract this paper presents a lyapunov formulation of the cyclic small gain theorem for dynamical networks composed of discrete time input to state stable iss subsystems iss lyapunov functions for dynamical networks satisfying the cyclic small gain condition are constructed from the iss lyapunov functions of the subsystems

robust exponential input to state stability of impulsive systems with an application in micro grids abstract this paper studies the robust exponential input to state stability robust e iss for impulsive systems new notions of input to state exponent is e and e property are proposed based on the established relation between is e and e property and the method of variation of constants formula the equivalent conditions for robust e iss have been derived then the notion of robust event e iss is defined the sufficient conditions and the robust regions for robust e iss and robust event e iss are also derived by using the is e of every subsystem it shows the whole system may have robust event e iss while every subsystem may have no iss it also shows the external disturbances may lead to relatively small robust regions the results are then specialized to derive the equivalent conditions of interval e iss for interval impulsive systems as an application the result is used to test the iss for a controlled micro grid

stability and robustness of quasi linear impulsive hybrid systems both hybrid dynamical systems and impulsive dynamical systems are studied extensively in the literature however impulsive hybrid systems are not yet well studied nonetheless many physical systems exhibit both system switching and impulsive jump phenomena this paper investigates stability and robust stability of a class of quasi linear impulsive hybrid systems by using the methods of lyapunov functions and riccati inequalities sufficient conditions for stability and robust stability of those systems are established some examples are given to illustrate the applicability of our results

subsets and subspaces several rules known to be valid within the set theory are revisited and considered from the point of view of the question whether they remain satisfied when sets are replaced with subspaces from c n 1 it is shown that some of the set relationships hold true upon such a replacement however there is also an extensive class of relationships whose validity is no longer guaranteed in this class the commutativity of the orthogonal projectors onto the involved subspaces proves to play an important role some related results inspired by probability theory are established as well

technical communique robust backstepping for the euler approximate model of sampled data strict feedback systems stabilization of uncertain sampled data strict feedback systems is addressed the stability study is carried out on the euler approximation of the exact discretized model of the plant firstly a class of state feedback controllers is developed that guarantees an input to state stability property for the closed loop system additionally assuming some hypotheses on the uncertain terms hold a practical asymptotic stability property is ensured by designing an appropriate class of controllers

nonlinear small gain theorems for discrete time feedback systems and applications we derive in this work a local nonlinear small gain theorem in the framework of input to state stability for discrete time systems our primary objective is to show that as in the continuous time context these discrete time nonlinear small gain theorems are very effective in stability analysis and synthesis for various classes of discrete time control systems two converse lyapunov theorems for discrete exponential stability are developed to assist these applications new results in stability and stabilization presented in this paper are significant extensions of previous work by other authors ieee trans automat control 38 1993 1398 39 1994 2340 33 1988 1082

hierarchical ensemble of global and local classifiers for face recognition in the literature of psychophysics and neurophysiology many studies have shown that both global and local features are crucial for face representation and recognition this paper proposes a novel face recognition method which exploits both global and local discriminative features in this method global features are extracted from the whole face images by keeping the low frequency coefficients of fourier transform which we believe encodes the holistic facial information such as facial contour for local feature extraction gabor wavelets are exploited considering their biological relevance after that fisher s linear discriminant fld is separately applied to the global fourier features and each local patch of gabor features thus multiple fld classifiers are obtained each embodying different facial evidences for face recognition finally all these classifiers are combined to form a hierarchical ensemble classifier we evaluate the proposed method using two large scale face databases feret and frgc version 2 0 experiments show that the results of our method are impressively better than the best known results with the same evaluation protocol

constructing projections on sums and intersections abstract in this note we list several formulas for computing orthogonal projections onto the linear sum and intersection of two subspaces of c n in terms of the projections on the individual subspaces

versions of sontag s input to state stability condition and the global stabilizability problem this paper deals with the global feedback stabilizability problem for interconnected nonlinear systems that are affine in the control the corresponding feedback stabilizers are supposed to be almost smooth real mappings the results of this paper extend those developed in recent works of the author siam j control optim 29 1991 pp 457 473 systems control lett 15 1990 pp 441 448 siam j control optim 30 1992 pp 879 893 concerning the local stabilizability problem the main sufficient conditions presented are of lyapunov type and the main idea of the paper is based on the input to state stability condition introduced by sontag ieee trans automat control 35 1990 pp 473 477

on finite time stability of cyclic switched nonlinear systems this technical note considers the global finite time stability problem for a class of switched nonlinear systems with the cyclic switching sequence dissipative or non dissipative impulsive effects may appear at each switching instant and each mode may or may not be finite time stable individually a new concept named cycle dwell time is proposed based on which two stability conditions are established these conditions fully reveal the trade off among each mode s dynamics impulsive dynamics and initial conditions an example of multi agent systems illustrates the efficiency of the new results

brief paper output feedback sampled data polynomial controller for nonlinear systems this paper presents the stability analysis and control synthesis for a sampled data control system which consists of a nonlinear plant and an output feedback sampled data polynomial controller connected in a closed loop the output feedback sampled data polynomial controller which can be implemented by a microcontroller or a digital computer is proposed to stabilize the nonlinear plant based on the lyapunov stability theory stability conditions in terms of sum of squares are obtained to guarantee the stability and to aid the design of a polynomial controller a simulation example is given to demonstrate the effectiveness of the proposed control approach

nn adaptive output feedback tracking control for a class of discrete time non affine systems with a dynamic compensator the problem of tracking control for a class of uncertain non affine discrete time nonlinear systems with internal dynamics is addressed the fixed point theorem is first employed to ensure the control problem in question is solvable and well defined based on it an adaptive output feedback control scheme based on neural network nn is presented the proposed control algorithm consists of two parts a dynamic compensator is introduced to stabilise the linear portion of the tracking error system a single hidden layer neural network shl nn approximation mechanism is introduced to cancel the uncertainties resulting from the non affine function where the recursive weight update rules of nn estimation are derived from the discrete time version of lyapunov control theory ultimate boundedness of the error signals is shown through lyapunov s direct method and the discrete time version of input to state stability iss theory finally a model of automatical underwater vehicle auv is considered to show the

robust global stabilisability by means of sampled data control with positive sampling rate this work proposes a notion of robust reachability of one set from another set under constant control this notion is used to construct a control strategy involving sequential set to set reachability which guarantees robust global stabilisation of non linear sampled data systems with positive sampling rate sufficient conditions for robust reachability of one set from another under constant control are also provided the proposed method is illustrated through a number of examples including the study of the sampled data stabilisation problem of the chemostat

design of discrete time nonlinear control systems via smooth feedback using the center manifold theory for maps in a systematic way the authors present in this note a necessary condition and sufficient conditions for discrete time nonlinear systems to be stabilizable via smooth state feedback then the authors derive a necessary and sufficient condition characterizing the existence of exponential observers for lyapunov stable discrete time nonlinear systems this in turn leads to a separation principle for the asymptotic stabilization problem as an application the output regulation problem is solved via error feedback

stability of uncertain quasi periodic hybrid dynamic systems this paper derives sufficient conditions for the stability of uncertain quasi periodic hybrid dynamic systems these conditions do not require the lyapunov function to be non increasing along each trajectory of the continuous variable dynamic system cvds in other words they do not require every cvds to be stable and they also do not require the lyapunov function to be non increasing along the whole sequence of the switchings furthermore they do not require the knowledge of the continuous trajectory with the proposed conditions the stability bounds for structured perturbations characterized by non negative matrices that still ensure robust stability are derived

quasi exponential input to state stability for discrete time impulsive hybrid systems this paper investigates the problem of input to state stability iss for the general discrete time impulsive hybrid systems quasi exponential input to state stability criteria are established for non linear discrete time impulsive hybrid systems based on the lyapunov function the results are then specialized to the linear discrete time impulsive hybrid systems and fairly simple algebraic conditions are derived moreover iss small gain properties are also investigated for a class of interconnected discrete time impulsive systems several examples are given to illustrate results

on a generalized core inverse abstract the paper introduces the concept of a generalized core inverse of a matrix which extends the notion of the core inverse defined by baksalary and trenkler 1 while the original core inverse is restricted to matrices of index one the generalized core inverse exists for any square matrix several properties of the new concept are identified with the derivations based essentially on partitioned representations of matrices some of the features of the generalized core inverse coincide with those attributed to the core inverse but there are also such which characterize the core inverse only and not its generalization

stability of higher order discrete time lur e systems abstract we consider discrete time lur e systems obtained by applying nonlinear feedback to a system of higher order difference equations arma models the arma model relates the inputs and outputs of the linear system and does not involve any internal or state variables a stability theory subsuming results of circle criterion type is developed including criteria for input to output stability a concept which is very much reminiscent of input to state stability

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

computation of local iss lyapunov functions for discrete time systems via linear programming abstract this paper presents a numerical algorithm for computing iss lyapunov functions for discrete time systems which are input to state stable iss on compact subsets of the state space the algorithm relies on solving a linear optimisation problem and delivers a continuous and piecewise affine iss lyapunov function on a suitable triangulation covering the given compact set excluding a small neighbourhood of the origin the objective of the linear optimisation problem is to minimise the iss gain it is shown that for every iss system there exists a suitable triangulation such that the proposed algorithm terminates successfully

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

accurate calculation of zernike moments zernike moments zms are very effective global image descriptors which are used in many digital image processing applications the digitization process compromises the accuracy of the moments and therefore several of its properties are affected there are two major discretization errors namely the geometric error and numerical integration error in this paper we propose two new algorithms which eliminate these errors the first algorithm performs the exact computation of geometric moments gms over a unit disk and then uses gms to zms relationship to compute the latter this algorithm is computationally more expensive and it becomes numerically instable for higher order moments therefore we develop a second algorithm based on gaussian quadrature numerical integration the second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of gaussian quadrature numerical integration increases the proposed algorithms are observed to provide very accurate zms which result in improved image reconstruction reduction in reconstruction error and improvement in rotation and scale invariance exhaustive experiments are provided to support improved accuracy of zms and time complexity analysis is performed for the existing and the proposed methods

viability control for a class of underactuated systems this paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality state constraints defining a constrained viability set k based on concepts from viability theory the necessary conditions for selecting viable controls for a nonholonomic system are given so that system trajectories starting in k always remain in k furthermore a class of state feedback control solutions for nonholonomic systems are redesigned by means of switching control so that system trajectories starting in k converge to a goal set g in k without ever leaving k the proposed approach can be applied in various problems whose objective can be recast as controlling a nonholonomic system so that the resulting trajectories remain forever in a subset k of the state space until they converge into a goal target set g in k the motion control for an underactuated marine vehicle in a constrained configuration set k is treated as a case study the set k essentially describes the limited sensing area of a vision based sensor system and viable control laws which establish convergence to a goal set g in k are constructed the robustness of the proposed control approach under a class of bounded external perturbations is also considered the efficacy of the methodology is demonstrated through simulation results

on stability of sets for sampled data nonlinear inclusions via their approximate discrete time models and summability criteria this paper consists of two main parts in the first part we provide a framework for stabilization of arbitrary not necessarily compact closed sets for sampled data nonlinear differential inclusions via their approximate discrete time models we generalize d nesic a r teel and p v kokotovic systems control lett 38 1999 pp 259 270 theorem 1 in several different directions we consider stabilization of arbitrary closed sets plants described as sampled data differential inclusions and arbitrary dynamic controllers in the form of difference inclusions our result does not require the knowledge of a lyapunov function for the approximate model which is a standing assumption in d nesic and a r teel ieee trans automat control 49 2004 pp 1103 1122 and d nesic a r teel and p v kokotovic systems control lett 38 1999 pp 259 270 theorem 2 we present checkable conditions that one can use to conclude semiglobal asymptotic stability or global exponential stability ges of the sampled data system via appropriate properties of its approximate discrete time model in the second part we present sufficient conditions for stability of parameterized difference inclusions that involve various summability criteria on trajectories of the system to conclude global asymptotic stability gas or ges and they represent discrete time counterparts of results given in a r teel e panteley and a loria math control signals systems 15 2002 pp 177 201 these summability criteria are not lyapunov based and they are tailored to be used within our above mentioned framework for stabilization of sampled data differential inclusions via their approximate discrete time models we believe that these tools will be a useful addition to the toolbox for controller design for sampled data nonlinear systems via their approximate discrete time models

stabilization of nonlinear discrete time systems using state detection some recent results concerning stabilization of continuous time systems using state detection are extended to the case of discrete time nonlinear systems it is shown that if a discrete time locally detectable system can be stabilized by a state feedback law then it can also be stabilized by a feedback law that depends on the output of a weak detector

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

image analysis by fractional order orthogonal moments orthogonal moments play an important role in image analysis and other similar applications however existing orthogonal moments are restricted to integer order and little investigation of non integer order orthogonal moments has been conducted to date in this paper a general framework of real order orthogonal moments also known as fractional order orthogonal moments is proposed in this general framework fractional order orthogonal moments can be defined in cartesian and polar coordinate systems shifted legendre polynomials are implemented in this paper to investigate the properties of fractional order orthogonal moments a series of experiments are performed which demonstrate that fractional order orthogonal moments are not only capable of region of interest roi feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition

stability analysis for a class of nonlinear discrete time control systems subject to disturbances and to actuator saturation this paper addresses the stability characterisation problem for a class of nonlinear discrete time control systems subject to actuator saturation and energy bounded disturbance inputs the considered class of systems covers all nonlinear discrete time systems that can be modelled by rational difference equations based on quadratic and piecewise quadratic lyapunov functions conditions based on linear matrix inequalities are proposed to analyse the asymptotic stability internal stability and the l2 input to state stability external stability of the closed loop system the proposed conditions are then incorporated into convex optimisation problems to either maximise an estimate of the region of attraction or a bound on the admissible l2 disturbances and also to obtain an estimate of the system l2 gain for an admissible set of disturbances

a framework for stabilization of nonlinear sampled data systems based on their approximate discrete time models a unified framework for design of stabilizing controllers for sampled data differential inclusions via their approximate discrete time models is presented both fixed and fast sampling are considered in each case sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete time plant models also stabilizes the exact discrete time plant model for sufficiently small integration and or sampling periods previous results in the literature are extended to cover 1 continuous time plants modeled as differential inclusions 2 general approximate discrete time plant models 3 dynamical discontinuous controllers modeled as difference inclusions and 4 stability with respect to closed arbitrary not necessarily compact sets

explicit design of time varying stabilizing control laws for a class of controllable systems without drift abstract this paper gives a systematic way to design time variant feedback control laws for a class of controllable nonlinear systems this class contains a lot of systems which cannot be stabilized via a time invariant feedback control law the interest of this work lies in the design method since a general existence results is already available the techniques employed here are basic they mainly involve classical lyapunov analysis

on hybrid impulsive and switching systems and application to nonlinear control in this note a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated using switched lyapunov functions some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established in addition a new hybrid impulsive and switching control strategy for nonlinear systems is developed a typical example the unified chaotic system is given to illustrate the theoretical results

a lyapunov approach to exponential stabilization of nonholonomic systems in power form in this paper a continuous feedback control law with time periodic terms is derived for the control of nonholonomic systems in power form the control law is derived by lyapunov design from a homogeneous lyapunov function global asymptotic stability is shown by applying the principle of invariance for time periodic systems exponential convergence follows since the vector fields are homogeneous of degree zero

on a subspace metric based on matrix rank abstract the metric between subspaces m n c n 1 defined by m n rk p m p n where rk denotes rank of a matrix argument and p m and p n are the orthogonal projectors onto the subspaces m and n respectively is investigated such a metric takes integer values only and is not induced by any vector norm by exploiting partitioned representations of the projectors several features of the metric m n are identified it turns out that the metric enjoys several properties possessed also by other measures used to characterize subspaces such as distance also called gap frobenius distance direct distance angle or minimal angle

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided

column space equalities for orthogonal projectors in their paper y tian g p h styan rank equalities for idempotent and involutory matrices linear algebra appl 335 2001 101 117 tian and styan established several rank equalities involving a pair of idempotent matrices p and q subsequently these results are reinvestigated from the point of view of the following question provided that idempotent p q are hermitian which relationships given in the aforementioned paper remain valid when ranks are replaced with column spaces simultaneously some related results are established which shed additional light on the links between subspaces attributed to various functions of a pair of orthogonal projectors

networked predictive control of uncertain constrained nonlinear systems recursive feasibility and input to state stability analysis in this paper the robust state feedback stabilization of uncertain discrete time constrained nonlinear systems in which the loop is closed through a packet based communication network is addressed in order to cope with model uncertainty time varying transmission delays and packet dropouts typically affecting the performances of networked control systems a robust control scheme combining model predictive control with a network delay compensation strategy is proposed in the context of non acknowledged udp like networks the contribution of the paper is twofold first the issue of guaranteeing the recursive feasibility of the optimization problem associated to the receding horizon control law has been addressed such that the invariance of the feasible region under the networked closed loop dynamics can be guaranteed secondly by exploiting a novel characterization of regional input to state stability in terms of time varying lyapunov functions the networked closed loop system has been proven to be input to state stable with respect to bounded perturbations

c sup algebra of strong limit power functions motivated by problems in robust control of power signal set h sub 2 e g h sub 2 is not a vector space fourier analysis cannot be carried out on h sub 2 in general we study those functions in h sub 2 which we call strong limit power we show that the set of all such functions is a sufficiently large c sup algebra fourier analysis is carried out on the functions in particular the uniqueness of the fourier expansion of a strong limit power function is established finally we point out how to analyze and reconstruct such functions

robust exponential stabilization for large scale uncertain impulsive systems with coupling time delays abstract in this paper we aim to study robust exponential stabilization for a large scale uncertain impulsive system with coupling time delays furthermore we also provide an estimation of the rate of convergence of exponential stabilization by utilizing the lyapunov method and razumikhin technique we shall design the feedback hybrid controllers in terms of linear matrix inequalities under which the robust exponential stability is achieved for a closed loop large scale uncertain impulsive system with coupling time delays moreover we shall also use the results obtained to design impulsive controllers for a large scale uncertain continuous system under which the closed loop continuous system achieves robust and exponential stability to illustrate our results one example is solved

formulas relating kl stability estimates of discrete time and sampled data nonlinear systems abstract we provide an explicit kl stability or input to state stability iss estimate for a sampled data nonlinear system in terms of the kl estimate for the corresponding discrete time system and a k function describing inter sample growth it is quite obvious that a uniform inter sample growth condition plus an iss property for the exact discrete time model of a closed loop system implies uniform iss of the sampled data nonlinear system our results serve to quantify these facts by means of comparison functions our results can be used as an alternative to prove and extend results in 1 or extend some results in 4 to a class of nonlinear systems finally the formulas we establish can be used as a tool for some other problems which we indicate

eigenvalues of functions of orthogonal projectors by representing two orthogonal projectors in a finite dimensional vector space as partitioned matrices several characterizations concerning eigenvalues of various functions of the pair are obtained these results substantially extend the ones already available in the literature additionally some related results dealing with the functions of a pair of orthogonal projectors are provided with the emphasis laying on the problem of invertibility

class kl estimates and input to state stability analysis of impulsive switched systems abstract in this paper we investigate input to state stability of impulsive switched systems the goal is to bridge two apparently different but both useful stability notions input to state stability and stability in terms of two measures in the hybrid systems setting based on two class kl function estimates and a comparison theorem for impulsive differential equations two sets of sufficient lyapunov type conditions for input to state stability in terms of two measures are obtained for impulsive switched systems these conditions exploit some nonlinear integral constraints in terms of generalized dwell time conditions to balance the continuous dynamics and impulsive dynamics so that input to state stability is achieved despite possible instability of individual continuous subsystems or destabilizing impulsive effects an illustrative example is presented together with numerical simulations to demonstrate the main results

on the projectors ff and f f abstract a particular version of the singular value decomposition is exploited for an extensive analysis of two orthogonal projectors namely ff and f f determined by a complex square matrix f and its moore penrose inverse f various functions of the projectors are considered from the point of view of their nonsingularity idempotency nilpotency or their relation to the known classes of matrices such as ep bi ep gp dr or sr this part of the paper was inspired by benitez and rakocevic j benitez v rakocevic matrices a such that aa a a are nonsingular appl math comput 217 2010 3493 3503 further characteristics of ff and f f with a particular attention paid on the results dealing with column and null spaces of the functions and their eigenvalues are derived as well besides establishing selected exemplary results dealing with ff and f f the paper develops a general approach whose applicability extends far beyond the characteristics provided therein

uniform stability of large scale delay discrete impulsive systems this article investigates the problem of uniform stability for the large scale delay dis discrete impulsive systems by establishing the comparison principle for the general delay dis uniform stability criteria are derived for three kinds linear affine and non linear of large scale delay dis the obtained criteria shows that the stability properties of non linear large scale delay dis can be derived by comparing to a linear and lower dimension delay dis with known stability properties some examples are given to illustrate results obtained by us

fast computation of krawtchouk moments the paper describes the calculation of the krawtchouk moments kms from an image which is a computationally demanding task we present two original methods that use the outputs of cascaded digital filters in deriving kms the first approach uses the digital filter outputs to form geometric moments gms and the kms are obtained via gms the second method uses a direct relationship to obtain kms from the digital filter outputs this is possible thanks to the formulation of krawtchouk polynomials in terms of binomial functions which are equivalent to the digital filter outputs in this study the performance of the proposed techniques is compared with other existing methods of kms calculation the experimental study shows that the first and the second proposed techniques perform 57 and 87 faster than the recurrence method for a real image of a size 128 128 pixels which performs a significant improvement

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem

on a pair of vector spaces the paper provides an extensive investigation of a pair of vectors spaces with a particular attention paid to perpendicular subspaces several new properties of the pair are identified some of which enabled to derive known facts about subspaces by means of simpler proofs the approach utilized exploits partitioned representations of orthogonal projectors and is based on the fact that there is one to one correspondence between an orthogonal projector and the subspace onto which it projects

input to state stability for discrete time delay systems via the razumikhin technique this paper aims to study the problem of input to state stability iss for discrete time delay systems by employing the razumikhin technique and suitable lyapunov functions backward and forward razumikhin type iss theorems that guarantee the global iss global asymptotic iss and global exponential iss for general discrete time delay systems are established moreover razumikhin type global exponential iss theorems give the estimation of the convergence speed as an application the razumikhin type exponential iss result is used to derive exponential iss criteria for a class of interconnected discrete systems with coupling time delays and disturbance inputs finally examples are given to illustrate the results

a systematic method for efficient computation of full and subsets zernike moments a new method is proposed for fast and accurate computation of zernike moments this method presents a novel formula for computing exact zernike moments by using exact complex moments where the exact values of complex moments are computed by mathematical integration of the monomials over digital image pixels the proposed method is applicable to compute the full set of zernike moments as well as the subsets of individual order repetition and an individual moment a comparison with other conventional methods is performed the results show the superiority of the proposed method

on optimal control problems of a class of impulsive switching systems with terminal states constraints abstract the global optimal control problem is proposed for a special class of hybrid dynamical systems i e impulsive switching systems then the necessary condition of the above problem the minimum principle is given ekeland s variational principle and the matrix cost functional structure expression are utilized in the process of the proof based on the main result a special linear hybrid impulsive and switching system hiss is illustrated and the optimal control algorithm is presented moreover the cases of pure impulsive systems and pure switched systems are included in this paper

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

quaternion moment and its invariants for color object classification moment invariants are important shape descriptors in computer vision in this study we propose new sets of quatemion moment descriptors for color image they are constructed in the quaternion framework and are an extension of complex moment invariants for grayscale images this is a useful tool in color image processing and color object recognition tasks that require the similarity invariance the advantage of the proposed quatemion moment invariants is that they can not only process color image in a holistic manner but also grayscale one in addition the computational complexity of the proposed method is much lower than the quaternion zernike moments defined in the polar coordinates an example of using the quaternion moment invariants as pattern features for a color object classification application is given theoretical and experimental results show that the proposed descriptors perform better than the other competing moment based methods c 2014 elsevier inc all rights reserved

face recognition the problem of compensating for changes in illumination direction a face recognition system must recognize a face from a novel image despite the variations between images of the same face a common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations examples of such representations are edge maps image intensity derivatives and images convolved with 2d gabor like filters here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination as well as viewpoint and facial expression our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination similar results were obtained for changes due to viewpoint and expression image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination however systems based only on such representations failed to recognize up to 20 percent of the faces in our database humans performed considerably better under the same conditions we discuss possible reasons for this superiority and alternative methods for overcoming illumination effects in recognition

near infrared face recognition using zernike moments and hermite kernels this work proposes a novel face recognition method based on zernike moments zms and hermite kernels hks to cope with variations in facial expression changes in head pose and scale occlusions due to wearing eyeglasses and the effects of time lapse near infrared images are used to tackle the impact of illumination changes on face recognition and a combination of global and local features is utilized in the decision fusion step in the global part zms are used as a feature extractor and in the local part the images are partitioned into multiple patches and filtered patch wise with hks finally principal component analysis followed by linear discriminant analysis is applied to data vectors to generate salient features and decision fusion is applied on the feature vectors to properly combine both global and local features experimental results on casia nir and polyu nir face databases clearly show that the proposed method achieves significantly higher face recognition accuracy compared with existing methods

robust stability of quasi periodic hybrid dynamic uncertain systems considers the robust stability of quasi periodic hybrid dynamic systems hdss with polytopic uncertainties the quasi periodic hdss has infinite switchings but the switching sequence forms a cycle and the cycle is repeated we derive the stability conditions for quasi periodic hds with uncertainties in continuous variable dynamic systems and with variations in both the switching conditional set and the reset map by analyzing the behavior of the system along the cycle the results require the lyapunov function to be bounded by a continuous function along each continuous variable dynamic system and is nonincreasing along a subsequence of the switchings they do not require the lyapunov function to be nonincreasing along the whole sequence of the switchings

exponential stabilization of driftless nonlinear control systems using homogeneous feedback this paper focuses on the problem of exponential stabilization of controllable driftless systems using time varying homogeneous feedback the analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control lie algebra it can be shown that any continuous time varying controller that achieves exponential stability relative to the euclidean norm is necessarily non lipschitz despite these restrictions we provide a set of constructive sufficient conditions for extending smooth asymptotic stabilizers to homogeneous exponential stabilizers the modified feedbacks are everywhere continuous smooth away from the origin and can be extended to a large class of systems with torque inputs the feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

feedback stabilization of dissipative impulsive dynamical systems in this paper we derive conditions under which a dissipative impulsive dynamical system is asymptotically stabilizable by a feedback controller specializing the obtained results to the case of dissipative linear impulsive dynamical systems with the quadratic supply rate we establish the corresponding sufficient conditions finally simulation results are given to demonstrate the effectiveness of our results

brief robust stabilization via iterative state steering with an application to chained form systems an approach is presented for the robust stabilization of non linear systems the proposed strategy can be adopted whenever it is possible to compute a control law that steers the state in finite time from any initial condition to a point closer to the desired equilibrium under suitable assumptions such control law can be applied in an iterative fashion obtaining uniform asymptotic stability of the equilibrium point with exponential rate of convergence small non persistent perturbations are rejected while persistent perturbations induce limited errors in order to show the usefulness of the presented theoretical developments the approach is applied to chained form systems and for illustration simulations results are given for the robust stabilization of a unicycle

gabor feature based classification using the enhanced fisher linear discriminant model for face recognition this paper introduces a novel gabor fisher 1936 classifier gfc for face recognition the gfc method which is robust to changes in illumination and facial expression applies the enhanced fisher linear discriminant model efm to an augmented gabor feature vector derived from the gabor wavelet representation of face images the novelty of this paper comes from 1 the derivation of an augmented gabor feature vector whose dimensionality is further reduced using the efm by considering both data compression and recognition generalization performance 2 the development of a gabor fisher classifier for multi class problems and 3 extensive performance evaluation studies in particular we performed comparative studies of different similarity measures applied to various classifiers we also performed comparative experimental studies of various face recognition schemes including our novel gfc method the gabor wavelet method the eigenfaces method the fisherfaces method the efm method the combination of gabor and the eigenfaces method and the combination of gabor and the fisherfaces method the feasibility of the new gfc method has been successfully tested on face recognition using 600 feret frontal face images corresponding to 200 subjects which were acquired under variable illumination and facial expressions the novel gfc method achieves 100 accuracy on face recognition using only 62 features