theory of markov systems with fuzzy states in this paper the theory of fuzzy logic is combined with the theory of markov systems and the concept of a markov system with fuzzy states is introduced for the first time the main objective is to develop a methodology of describing a markov population system with fuzzy states this is an effort to deal with the fact that in real applications one is often faced with fuzzy states this paper investigates the properties of a markov system with states that have imprecise boundaries a full description of a nonhomogeneous markov system with fuzzy states is outlined and the basic parameters of the system are provided more specifically the expected population structure of the system is found and given in a closed analytic form and the asymptotic behaviour of the system is provided under the more realistic assumption of a fuzzy set space

on equivalence of two stability criteria for continuous time switched systems with dwell time constraint in this note a study on the equivalence of two stability criteria for continuous time switched linear systems with dwell time constraint is presented it is demonstrated that for any dwell time satisfying the conditions in stability criterion proposed in geromel and colaneri 2006 the conditions in stability criterion of allerhand and shaked 2011 also hold as long as the number of decision variables and related lmis is sufficiently large which implies the two stability criteria are intrinsically equivalent the equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and lmis a numerical example is proposed to illustrate the theoretical results and an extension to uncertain case is briefly presented

fuzzy markovian decision process in this paper a markovian decision process with fuzzy states is considered it is shown that if the markov chain associated with the process of non fuzzy states is irreducible then the corresponding markov chain associated with the fuzzy states is also irreducible the importance of this result lies in the fact that the traditional methods for solving the markovian decision process can be used in the case with fuzzy states also

characterization and computation of disturbance invariant sets for constrained switched linear systems with dwell time restriction this paper introduces the concept and characterization of disturbance dwell time invariance ddt invariance and constraint admissible ddt invariance caddt invariance for constrained systems with additive disturbance under dwell time switching using the characterization necessary and sufficient conditions for ddt invariance and algorithms for the computation of the minimal and maximal constraint admissible convex ddt invariant sets are provided numerical examples of such sets for several systems are also provided

infinite products of matrices with some negative elements and row sums equal to one abstract infinite products of a class of matrices the v matrices with some negative elements and row sums equal to one are studied after a series of lemmas and propositions a basic theorem is provided where it is shown that the limit of an infinite product of v matrices under certain conditions exists finally a method for finding this limit based on some properties of generalized inverses is provided

robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

positive filtering for continuous time positive systems under l 1 performance in this paper we address the positive filtering problem for positive continuous time systems under the l1 induced performance a pair of positive filters with error bounding feature is proposed to estimate the output of positive systems a novel characterisation is first obtained to ensure that the filtering error system is asymptotically stable with a prescribed l1 induced performance then necessary and sufficient conditions for the existence of required filters are presented and the obtained results are expressed in terms of linear programming problems which can be easily checked by standard software finally a numerical example is given to illustrate the effectiveness of the proposed design procedures

co positive lyapunov functions for the stabilization of positive switched systems in this paper exponential stabilizability of continuous time positive switched systems is investigated for two dimensional systems exponential stabilizability by means of a switching control law can be achieved if and only if there exists a hurwitz convex combination of the metzler system matrices in the higher dimensional case it is shown by means of an example that the existence of a hurwitz convex combination is only sufficient for exponential stabilizability and that such a combination can be found if and only if there exists a smooth positively homogeneous and co positive control lyapunov function for the system in the general case exponential stabilizability ensures the existence of a concave positively homogeneous and co positive control lyapunov function but this is not always smooth the results obtained in the first part of the paper are exploited to characterize exponential stabilizability of positive switched systems with delays and to provide a description of all the switched equilibrium points of an affine positive switched system

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

on stability and h control of switched systems with random switching signals abstract in this paper the stability analysis and h control problems for a class of continuous time switched systems with a random switching signal are addressed the dwell time of the switched systems is characterized with a fixed part and a random part a new stability criterion which is equivalent to a necessary and sufficient condition developed previously is established first and then it is reformulated in terms of linear matrix inequalities based on the stability analysis result l 2 gain performance analysis and h control problems are studied several numerical examples are given to illustrate the effectiveness of our results

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

on l1 gain control of 2 d positive roesser systems with directional delays necessary and sufficient conditions abstract in this paper the problem of l 1 gain control is addressed for two dimensional 2 d positive roesser systems with directional delays a complete solution to the design problem is presented for the first time specifically by exploiting a new approach based on 2 d z transform an exact value of l 1 induced norm of the input output operator is obtained this analytical result is utilized to derive necessary and sufficient conditions under which a 2 d positive system with delays is asymptotically stable with a prescribed l 1 gain performance then by utilizing a vertex optimization approach necessary and sufficient conditions are established for the existence of a state feedback controller sfc that makes the closed loop system positive and stable subject to l 1 induced performance the proposed synthesis conditions are formulated in terms of linear programming lp which can be effectively solved by various convex algorithms to minimize the l 1 performance index

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

the perturbed nonhomogeneous markov system abstract in this paper we introduce for the first time the concept of a perturbed nonhomogeneous markov system p nhms the expected population structure is found and its asymptotic behavior is provided under more realistic assumptions than previous studies by relaxing the assumption that the imbedded nonhomogeneous markov chain of a nhms is converging to a homogeneous markov chain also we study the sensitivity of the limiting expected structure on perturbations of the limiting input probabilities for a nhms moreover the asymptotic behavior of the variances and covariances of the class sizes of a p nhms is considered and found in an elegant closed analytic form

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

periodicity of infinite products of matrices with some negative elements and row sums equal to one abstract the problem of periodicity for the infinite products of a class of matrices the v matrices with some negative elements and row sums equal to one is studied after a series of lemmas propositions and theorems a basic theorem is proved that an infinite product of v matrices under certain conditions splits into a number of subsequences which converge geometrically fast finally a method for finding these limits based on some properties of generalized inverses is provided

brief paper stability of switched positive linear systems with average dwell time switching in this paper the stability analysis problem for a class of switched positive linear systems splss with average dwell time switching is investigated a multiple linear copositive lyapunov function mlclf is first introduced by which the sufficient stability criteria in terms of a set of linear matrix inequalities are given for the underlying systems in both continuous time and discrete time contexts the stability results for the splss under arbitrary switching which have been previously studied in the literature can be easily obtained by reducing mlclf to the common linear copositive lyapunov function used for the system under arbitrary switching those systems finally a numerical example is given to show the effectiveness and advantages of the proposed techniques

deterministic annealing for density estimation by multivariate normal mixtures an approach to maximum likelihood density estimation by mixtures of multivariate normal distributions for large high dimensional data sets is presented conventionally that problem is tackled by notoriously unstable expectation maximization em algorithms we remove these instabilities by the introduction of soft constraints enabling deterministic annealing our developments are motivated by the proof that algorithmically stable fuzzy clustering methods that are derived from statistical physics analogs are special cases of em procedures

stabilization of switched positive system with impulse and marginally stable subsystems a mode dependent dwell time method abstract in this article the problem of stabilization for the switched positive linear system spls with impulse and marginally stable subsystems is studied in which both the continuous time case and the discrete time case are taken into account by the usage of a piecewise weak linear copositive lyapunov function lclf and the mode dependent dwell time mdt time dependent switching control laws are designed to guarantee the asymptotic stability of the system furthermore based on the comparison principal for positive systems the main results are generalized to the time variant spls two examples are worked out to indicate that our results have advantages over some known results in the literature

solvability of static output feedback stabilization for lti positive systems abstract this paper addresses the stabilization problem of positive linear systems which have nonnegative states whenever the initial conditions are nonnegative the synthesis of static output feedback controllers that ensure the positivity and asymptotic stability of the closed loop system is investigated it is shown that this important problem is completely solved for single input and single output positive systems the proposed approach can be applied to multi input positive systems with controllers having one rank gains all the provided conditions are necessary and sufficient and can be solved in terms of linear programming

stability and boldsymbol l_ 1 gain analysis for positive takagi sugeno fuzzy systems with impulse this paper is concerned with the stability analysis and l 1 gain characterization for positive takagi sugeno fuzzy systems subject to impulse effects the main tool utilized is the construction of an impulse time dependent discretized copositive lyapunov function where the impulse interval partitioning idea is exploited to derive less conservative results for the disturbance free case stability criteria are developed to guarantee global exponential stability of the concerned systems under ranged and constant dwell time constraints the analysis of the influence of the discretizing parameter on the reduction of conservativeness is performed we further employ the proposed impulse time dependent discretized copositive lyapunov function to analyze the l 1 gain performance for the case where external disturbances are considered by performing a grid search for a scalar in an interval all the proposed criteria can be checked via linear programming finally numerical simulations are discussed to illustrate the effectiveness of the theoretical results

rate of convergence asymptotically attainable structures and sensitivity in non homogeneous markov systems with fuzzy states this paper is concerned with the rate of convergence the asymptotically attainable structures and the sensitivity of a non homogeneous markov system nhms in short with fuzzy states more specifically it is proved that under some realistic assumptions easily met in practice the convergence rate of the relative population structure to its limit is geometric furthermore the asymptotically attainable structures in a nhms with fuzzy states are given more precisely the problem of finding which states are possible as limiting ones in a nhms with fuzzy states is studied provided that the limit of the sequence of the input probability vectors is controlled moreover the sensitivity of the limiting expected population structure on perturbations of the limiting input probabilities for the system is also studied two applications in cognitive science and in manpower planning are given where the sensitivity of two nhms with three states is studied provided that the limiting input probability vector is perturbed

fuzzy semi markov migration process in credit risk we explore the rating system used by credit agencies with a focus on problems that justify the use of fuzzy set theory we prove that a fuzzy market is viable if and only if an equivalent martingale measure exists from which we construct the forward probability measure and under which the discounted price of a default free bond is a martingale we model the evolution of credit migration of a defaultable bond as an inhomogeneous semi markov process with fuzzy states we study the effects of changing the real probability measure to a forward probability measure in addition we investigate the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default finally we discuss parameter estimation and calibration of the inhomogeneous markov chain with fuzzy states

non weighted quasi time dependent h filtering for switched linear systems with persistent dwell time this paper is concerned with h filtering for a class of switched linear systems in discrete time domain a more general class of switching signals the persistent dwell time pdt switching is considered rather than the dwell time or average dwell time switching often studied in the literature the concept on a stage of switching in the type of pdt switching signals is introduced and each stage consists of a period of persistence and a dwell time portion in which no switching occurs a proper lyapunov function suitable to the pdt switching is constructed which is not only mode dependent but also quasi time dependent qtd then a qtd filter is designed such that the resulting filtering error system is globally uniformly asymptotically stable and has a guaranteed h noise attenuation performance certain techniques are explored such that the obtained performance index is of strictly non weighted h norm which contrasts with the weighted or called exponential ones i e weaker noise attenuation in the existing literature of switched systems with average dwell time an example of mass spring system is provided to show the validity and potential of the developed results

stability analysis of positive switched linear systems with delays this technical note addresses the stability problem of delayed positive switched linear systems whose subsystems are all positive both discrete time systems and continuous time systems are studied in our analysis the delays in systems can be unbounded under certain conditions several stability results are established by constructing a sequence of functions that are positive monotonically decreasing and convergent to zero as time tends to infinity additionally continuous for continuous time systems it turns out that these functions can serve as an upper bound of the systems trajectories starting from a particular region finally a numerical example is presented to illustrate the obtained results

a two layer mixture model of gaussian process functional regressions and its mcmc em algorithm the mixture of gaussian processes gps is capable of learning any general stochastic process based on a given set of sample curves for the regression and prediction problems however it is ineffective for curve clustering and prediction when the sample curves are derived from different stochastic processes as independent sources linearly mixed together in this paper we propose a two layer mixture model of gp functional regressions gpfrs to describe such a mixture of general stochastic processes or independent sources especially for curve clustering and prediction specifically in the lower layer the mixture of gpfrs mgpfrs is developed for a cluster or class of curves within the input space in the higher layer the mixture of mgpfrs is further established to divide the curves into clusters according to its components in the output space for the parameter estimation of the two layer mixture of gpfrs we develop a monte carlo em algorithm based on a monte carlo markov chain mcmc method in short the mcmc em algorithm we validate the hierarchical mixture of gpfrs and mcmc em algorithm using synthetic and real world data sets our results show that our new model outperforms the conventional mixture models in curve clustering and prediction

asymptotic variability of nonhomogeneous markov systems under cyclic behaviour abstract in this paper the asymptotic variability of nonhomogeneous markov systems under cyclic behaviour is studied it is found that the sequence of vectors of means variances and covariances splits into d subsequences which converge where d is the period of the cyclic finally an illustration of the present results with data from a manpower system is given

the byy annealing learning algorithm for gaussian mixture with automated model selection bayesian ying yang byy learning has provided a new mechanism that makes parameter learning with automated model selection via maximizing a harmony function on a backward architecture of the byy system for the gaussian mixture however since there are a large number of local maxima for the harmony function any local searching algorithm such as the hard cut em algorithm does not work well in order to overcome this difficulty we propose a simulated annealing learning algorithm to search the global maximum of the harmony function being expressed as a kind of deterministic annealing em procedure it is demonstrated by the simulation experiments that this byy annealing learning algorithm can efficiently and automatically determine the number of clusters or gaussians during the learning process moreover the byy annealing learning algorithm is successfully applied to two real life data sets including iris data classification and unsupervised color image segmentation

cal h _ infty and dwell time specifications of continuous time switched linear systems this technical note deals with continuous time switched linear systems and addresses the problem of characterizing open loop switching strategies based on dwell time specifications assuring a pre specified root mean square gain rms as a natural consequence of treating general systems of this particular class in terms of order and number of subsystems only sufficient conditions are worked out however as positive features they are expressed through linear matrix inequalities lmi being thus numerically solvable in polynomial time and allow the treatment of stable switched linear systems which do not admit a common lyapunov function the conservativeness of the proposed design method is evaluated by comparison with other results available in the literature by means of two simple illustrative examples

positivity exponential stability and disturbance attenuation performance for singular switched positive systems with time varying distributed delays abstract this article analyzes the singular switched positive systems with time varying distributed delays from the perspective of positivity exponential stability and disturbance attenuation performance referring to both l1 gain and l gain for the system a sufficient and necessary positivity condition is firstly developed by using the singular value decomposition technique then a sufficient condition of exponential stability which makes the considered system exponentially stable is proposed on the basis of co positive lyapunov krasovskii functional and average dwell time techniques and the obtained exponential decay rate can be adjusted in the light of various actual situations furthermore the article analyzes the disturbance attenuation performance referring to both l1 gain and l gain and through the convex optimization approach the optimal l1 gain and l gain performance level could be established respectively three examples are finally presented to show the feasibility and effectiveness of the obtained results

on a problem in population structure abstract the paper deals with a markov process that describes the age distribution in a population the limit distribution is well known we are here concerned with the speed of convergence second largest eigenvalue the exposition is independent of the theory of nonnegative matrices

stabilization of continuous time fractional positive systems by using a lyapunov function the stabilization problem for continuous time fractional linear systems with the additional condition of non negativity of the states is solved the obtained results are based on a direct lyapunov function in particular the synthesis of state feedback controllers is obtained by giving conditions in terms of linear programs the solution is also extended to stabilization by asymmetric bounded control illustrative examples are provided to show the usefulness of the results

asymptotically attainable structures in nonhomogeneous markov systems in this paper we provide and study a new aspect in the classical problem of the asymptotic behavior of a nonhomogeneous markov system nhms the set of asymptotically attainable structures is determined as the convex hull of k vertices which are given also the rate of convergence to asymptotically attainable structures is studied and conditions are provided for the convergence to be geometrically fast finally an illustration of the results with data from manpower systems is provided

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

lmi approach to linear positive system analysis and synthesis abstract this paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities lmis we first show that the celebrated perron frobenius theorem can be proved concisely by a duality based argument again by duality we next clarify a necessary and sufficient condition under which a hurwitz stable metzler matrix admits a diagonal lyapunov matrix with some identical diagonal entries as the solution of the lyapunov inequality this new result leads to an alternative proof of the recent result by tanaka and langbort on the existence of a diagonal lyapunov matrix for the lmi characterizing the h performance of continuous time positive systems in addition we further derive a new lmi for the h performance analysis where the variable corresponding to the lyapunov matrix is allowed to be non symmetric we readily extend these results to discrete time positive systems and derive new lmis for the h performance analysis and synthesis we finally illustrate their effectiveness by numerical examples on robust state feedback h controller synthesis for discrete time positive systems affected by parametric uncertainties

necessary and sufficient condition for stability of switched uncertain linear systems under dwell time constraint in this technical note a necessary and sufficient stability criterion for switched linear systems under dwell time constraint is proposed by employing a class of time scheduled homogeneous polynomial lyapunov functions with a sufficiently large degree the key feature of this nonconservative condition lies in its convexity in the system matrices which explicitly facilitates its further extension to uncertain systems then in order to obtain numerically testable condition a family of lmi conditions are presented with the aid of the idea of dividing the dwell time interval into a finite number of segments it is proved that the non conservativeness can be maintained with a sufficiently large interval dividing parameter in the end the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices numerical examples are presented to illustrate our findings

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

positivity of discrete singular systems and their stability in this paper we present an efficient approach to the analysis of discrete positive singular systems one of our main objectives is to investigate the problem of characterizing positivity of such systems previously this issue was not completely addressed we provide easily checkable necessary and sufficient conditions for such problem to be solved on the other hand we study the stability of discrete positive singular systems note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone all the conditions we provide are necessary and sufficient and are based on a reliable computational approach via linear programming

a nonconservative lmi condition for stability of switched systems with guaranteed dwell time ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems several methods have been proposed in the literature to address this problem but unfortunately they provide sufficient conditions only this technical note proposes the use of homogeneous polynomial lyapunov functions in the non restrictive case where all the subsystems are hurwitz showing that a sufficient condition can be provided in terms of an lmi feasibility test by exploiting a key representation of polynomials several properties are proved for this condition in particular that it is also necessary for a sufficiently large degree of these functions as a result the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well some examples illustrate the proposed approach

maximum certainty data partitioning abstract problems in data analysis often require the unsupervised partitioning of a dataset into clusters many methods exist for such partitioning but most have the weakness of being model based most assuming hyper ellipsoidal clusters or computationally infeasible in anything more than a three dimensional data space we re consider the notion of cluster analysis in information theoretic terms and show that minimisation of partition entropy can be used to estimate the number and structure of probable data generators

l1 gain performance analysis and positive filter design for positive discrete time markov jump linear systems a linear programming approach abstract this paper is concerned with the l 1 gain performance analysis and positive filter design for a positive discrete time markov jump linear system mjls by using a linear programming lp approach first by constructing a linear stochastic lyapunov function and introducing an equivalent deterministic positive discrete time linear system necessary and sufficient conditions in the form of lp are derived for stochastic stability and l 1 gain performance of the positive discrete time mjls then a sufficient condition on the existence of the desired positive l 1 gain filter is provided the desired positive l 1 gain filter can be designed by solving a standard lp problem the pest s structured population dynamic model is employed to illustrate the effectiveness of the proposed method

stability analysis and l1 gain characterization for switched positive systems under dwell time constraint abstract this paper deals with the problems of stability analysis and l 1 gain characterization for continuous time switched systems consisting of positive subsystems with the aid of a discretized copositive lyapunov function a sufficient condition ensuring the asymptotic stability of continuous time switched positive systems under dwell time constraint is obtained which can be checked via linear programming furthermore the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive lyapunov function is obtained the result is then extended to l 1 gain characterization for switched positive systems with a prescribed dwell time an unweighted l 1 gain can be computed via solving a linear programming problem a numerical example and a practical traffic example are given to illustrate our results

robust clustering by detecting density peaks and assigning points based on fuzzy weighted k nearest neighbors clustering by fast search and find of density peaks referred to as dpc was introduced by alex rodriguez and alessandro laio the dpc algorithm is based on the idea that cluster centers are characterized by having a higher density than their neighbors and by being at a relatively large distance from points with higher densities the power of dpc was demonstrated on several test cases it can intuitively find the number of clusters and can detect and exclude the outliers automatically while recognizing the clusters regardless of their shape and the dimensions of the space containing them however dpc does have some drawbacks to be addressed before it may be widely applied first the local density i of point i is affected by the cutoff distance dc and is computed in different ways depending on the size of datasets which can influence the clustering especially for small real world cases second the assignment strategy for the remaining points after the density peaks that is the cluster centers have been found can create a domino effect whereby once one point is assigned erroneously then there may be many more points subsequently mis assigned this is especially the case in real word datasets where there could exist several clusters of arbitrary shape overlapping each other to overcome these deficiencies a robust clustering algorithm is proposed in this paper to find the density peaks this algorithm computes the local density i of point i relative to its k nearest neighbors for any size dataset independent of the cutoff distance dc and assigns the remaining points to the most probable clusters using two new point assignment strategies the first strategy assigns non outliers by undertaking a breadth first search of the k nearest neighbors of a point starting from cluster centers the second strategy assigns outliers and the points unassigned by the first assignment procedure using the technique of fuzzy weighted k nearest neighbors the proposed clustering algorithm is benchmarked on publicly available synthetic and real world datasets which are commonly used for testing the performance of clustering algorithms the clustering results of the proposed algorithm are compared not only with that of dpc but also with that of several well known clustering algorithms including affinity propagation ap density based spatial clustering of applications with noise dbscan and k means the benchmarks used are clustering accuracy acc adjusted mutual information ami and adjusted rand index ari the experimental results demonstrate that our proposed clustering algorithm can find cluster centers recognize clusters regardless of their shape and dimension of the space in which they are embedded be unaffected by outliers and can often outperform dpc ap dbscan and k means