discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

adaptive control of linear systems with markov perturbations the stochastic model considered is a linear jump diffusion process x for which the coefficients and the jump processes depend on a markov chain z with finite state space first we study the optimal filtering and control problem for these systems with non gaussian initial conditions given noisy observations of the state x and perfect measurements of z we derive a new sufficient condition which ensures the existence and the uniqueness of the solution of the nonlinear stochastic differential equations satisfied by the output of the filter we study a quadratic control problem and show that the separation principle holds next we investigate an adaptive control problem for a state process x defined by a linear diffusion for which the coefficients depend on a markov chain the processes x and z being observed in independent white noises suboptimal estimates for the process x z and approximate control law are investigated for a large class of probability distributions of the initial state asymptotic properties of these filters and this control law are obtained upper bounds for the corresponding error are given

classification of matrix product unitaries with symmetries we prove that matrix product unitaries with on site unitary symmetries are completely classified by the chiral index and the cohomology class of the symmetry group g provided that we can add trivial and symmetric ancillas with arbitrary on site representations of g if the representations in both system and ancillas are fixed to be the same we can define symmetry protected indices spis which quantify the imbalance in the transport associated to each group element and greatly refines the classification these spis are stable against disorder and measurable in interferometric experiments our results lead to a systematic construction of two dimensional floquet symmetry protected topological phases beyond the standard classification and thus shed new light on understanding nonequilibrium phases of quantum matter

robust l_ infty induced filtering and control of stochastic systems with state multiplicative noise linear continuous time systems with stochastic uncertainties in their state space model are considered the problems of induced l state feedback control and filtering are solved for the stationary case in both problems the cost function is defined to be the expected value of the standard induced l performance index with respect to the uncertain parameters an example that demonstrates the applicability of the theory is given

stochastic h2 h control with x u v dependent noise finite horizon case in this paper the finite horizon mixed h 2 h control problem is studied for the systems governed by ito type nonlinear stochastic differential equations with state control and external disturbance dependent noise it is shown that the mixed h 2 h control under consideration is associated with the four cross coupled hamilton jacobi equations a discrete approximation algorithm is presented for solving the coupled generalized differential riccati equations arising from linear stochastic h 2 h control a necessary condition and a sufficient condition for the existence of the finite horizon stochastic h 2 h control are derived in particular some previous results on deterministic and stochastic h 2 h control can be viewed as corollaries of our main theorems

closed loop model set validation under a stochastic framework this paper deals with probabilistic model set validation it is assumed that the dynamics of a multi input multi output mimo plant is described by a model set with unstructured uncertainties and identification experiments are performed in closed loop a necessary and sufficient condition has been derived for the consistency of the model set with both the stabilizing controller and closed loop frequency domain experimental data fded in this condition only the euclidean norm of a complex vector is involved and this complex vector depends linearly on both the disturbances and the measurement errors based on this condition an analytic formula has been derived for the sample unfalsified probability sup of the model set some of the asymptotic statistical properties of the sup have also been briefly discussed a numerical example is included to illustrate the efficiency of the suggested method in model set quality evaluation

generalized differential riccati equation and indefinite stochastic lq control with cross term a stochastic indefinite linear quadratic lq optimal control problem with cross term in a finite time horizon is studied a new generalized differential riccati equation gdre is introduced it is shown that the solvability of the gdre is equivalent to the solvability of the indefinite stochastic lq problem furthermore all of the optimal controls including feedback and open loop can be identified via the solution to the gdre an example is presented to illustrate the theory obtained

weighted minimum and maximun operations in fuzzy sets theory abstract this short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians and corrects a misleading statement about it

voltage control for uncertain stochastic nonlinear system with application to energy internet non fragile robust h approach abstract in this paper a robust control method is used to intelligently regulate the dc bus voltage deviation for an islanded microgrid mg within the scenario of energy internet ei in order to cope with the uncertain and nonlinear nature of the power exchange in ei a new mathematical model is formulated to present the dynamics of the islanded mg where the state equation is expressed by a class of nonlinear stochastic differential equations sdes with parameter uncertainties appearing in system coefficients and the controllers specifically the nonlinearities appear in both drift and diffusion parts of such sdes our aim is to design a controller such that the effects of the modelling uncertainty and the external disturbance to the dc bus voltage of the off grid mg are minimized mathematically this can be regarded as problems of solving the non fragile robust stochastic stabilization and non fragile robust h control both of which can be solved via the linear matrix inequality lmi approach sufficiently we emphasize such new control system with its solution can also be applied into fields of industry economics etc based on real world data numerical results are illustrated and simulations show that our target is achieved

robust reduced order h output feedback control of retarded stochastic linear systems a method for designing reduced order output feedback controllers for linear time invariant retarded systems with state multiplicative wiener type noise is introduced which achieves a minimum bound on the h performance level a cost function is defined that is the expected value of the standard h performance cost with respect to the stochastic parameters a solution is thus obtained for the reduced order h output feedback control problem for the stationary case via the input output approach where the system is replaced by a non retarded one that contains deterministic norm bounded uncertainties the results achieved for the nominal case are extended to the uncertain case where the system matrices reside in a given polytope a numerical example taken from the field of aircraft control is given that demonstrates the applicability of the theory developed

the filtering problem for continuous time linear systems with markovian switching coefficients abstract the stochastic model under consideration is a markovian jump process with finite state space feeding the parameters of a linear diffusion process x the processes y and z observe linearly and separately x and in independent white noises some properties of the finite optimal filter for the x and processes given the history of measurements z are investigated apart from their theoretical interest these results have an interesting practical bearing on the general filtering problem by providing a natural finite suboptimal solution preliminary experimental results show the effectiveness of our approach to estimate the state trajectory even with a relatively low signal to noise ratio on the measurement processes

maximal versus strong solution to algebraic riccati equations arising in infinite markov jump linear systems abstract we deal with a perturbed algebraic riccati equation in an infinite dimensional banach space which appears for instance in the optimal control problem for infinite markov jump linear systems from now on imjls infinite or finite here has to do with the state space of the markov chain being infinite countable or finite see e g m d fragoso j baczynski optimal control for continuous time lq problems with infinite markov jump parameters siam j control optim 40 1 2001 270 297 by using a certain concept of stochastic stability a sort of l 2 stability we have proved in j baczynski m d fragoso maximal solution to algebraic riccati equations linked to infinite markov jump linear systems internal report lncc no 6 2006 existence and uniqueness of maximal solution for this class of equations as it is noticed in this paper unlike the finite case including the linear case we cannot guarantee anymore that maximal solution is a strong solution in this setting via a discussion on the main mathematical hindrance behind this issue we devise some mild conditions for this implication to hold specifically our main result here is that under stochastic stability along with a condition related with convergence in the infinite dimensional scenario and another one related to spectrum weaker than spectral continuity we ensure the maximal solution to be also a strong solution these conditions hold trivially in the finite case allowing us to recover the result of strong solution of c e de souza m d fragoso on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control systems control lett 14 1990 233 239 set for mjls the issue of whether the convergence condition is restrictive or not is brought to light and together with some counterexamples unveil further differences between the finite and the infinite countable case

l2 l filtering for stochastic systems driven by poisson processes and wiener processes this paper investigates the l2 l filtering problem for stochastic systems driven by poisson processes and wiener processes firstly this paper presents an approach to transform the expectation of stochastic integral with respect to poisson process into the expectation of lebesgue integral by the martingale theory then based on this a filter is designed to guarantee that the filtering error system is mean square asymptotically stable and its l2 l performance satisfies a prescribed level finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

robust kalman filters for linear time varying systems with stochastic parametric uncertainties we present a robust recursive kalman filtering algorithm that addresses estimation problems that arise in linear time varying systems with stochastic parametric uncertainties the filter has a one step predictor corrector structure and minimizes an upper bound of the mean square estimation error at each step with the minimization reduced to a convex optimization problem based on linear matrix inequalities the algorithm is shown to converge when the system is mean square stable and the state space matrices are time invariant a numerical example consisting of equalizer design for a communication channel demonstrates that our algorithm offers considerable improvement in performance when compared with conventional kalman filtering techniques

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

robust h estimation of stationary discrete time linear processes with stochastic uncertainties the problem of h filtering of stationary discrete time linear systems with stochastic uncertainties in the state space matrices is addressed where the uncertainties are modeled as white noise the relevant cost function is the expected value with respect to the uncertain parameters of the standard h performance a previously developed stochastic bounded real lemma is applied that results in a modified riccati inequality this inequality is expressed in a linear matrix inequality form whose solution provides the filter parameters the method proposed is applied also to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h2 h filtering for the above system is also treated the theory developed is demonstrated by a simple tracking example

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

robust fuzzy filter design for a class of nonlinear stochastic systems this paper describes the robust hinfin fuzzy filtering design for a class of nonlinear stochastic systems the system dynamic is modelled by itocirc type stochastic differential equations for general nonlinear stochastic systems the hinfin filter can be obtained by solving a second order nonlinear hamilton jacobi inequality in general it is difficult to solve the second order nonlinear hamilton jacobi inequality in this paper using fuzzy approach takagi sugeno t s fuzzy model the hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities lmis instead of a second order hamilton jacobi inequality when the worst case fuzzy disturbance is considered a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error the near minimum variance fuzzy filtering problem under the worst case fuzzy disturbance is also characterized in terms of linear matrix inequality problem lmip which can be efficiently solved by the convex optimization techniques simulation examples are provided to illustrate the design procedure and expected performance

optimal control for infinite dimensional stochastic differential equations with infinite markov jumps and multiplicative noise abstract in this paper we solve an infinite horizon linear quadratic control problem for a class of differential equations with countably infinite markov jumps and multiplicative noise the global solvability of the associated differential riccati type equations is studied under detectability hypotheses a nonstochastic operatorial approach is used some properties of the linear stochastic systems such as stability stabilizability and detectability are also discussed on the basis of a new solution representation result a generalized ito s formula which applies to infinite dimensional stochastic differential equations with countably infinite markov jumps is also provided

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

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

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

h 2 optimal filtering for continuous time periodic linear stochastic systems with state dependent noise abstract this note addresses the problem of optimal h 2 filtering for a class of continuous time time varying stochastic systems the time variation character is considered to be periodic the state space representation of the optimal filter is designed based on the unique periodic solution of a suitable lyapunov differential equation and the periodic and stabilizing solution of a suitable generalized periodic riccati differential equation some numerical experiments are also added to show the effectiveness of the proposed method

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

a numerical procedure to compute the stabilising solution of game theoretic riccati equations of stochastic control in this article the problem of the numerical computation of the stabilising solution of the game theoretic algebraic riccati equation is investigated the riccati equation under consideration occurs in connection with the solution of the h control problem for a class of stochastic systems affected by state dependent and control dependent white noise and subjected to markovian jumping the stabilising solution of the considered game theoretic riccati equation is obtained as a limit of a sequence of approximations constructed based on stabilising solutions of a sequence of algebraic riccati equations of stochastic control with definite sign of the quadratic part the proposed algorithm extends to this general framework the method proposed in lanzon feng anderson and rotkowitz lanzon a feng y anderson b d o and rotkowitz m 2008 computing the positive stabilizing solution to algebraic riccati equations with an indefinite quadratic term viaa recursive method ieee transactions on automat

lyapunov coupled equations for continuous time infinite markov jump linear systems this paper deals with lyapunov equations for continuous time markov jump linear systems mjls out of the bent which wends most of the literature on mjls we focus here on the case in which the markov chain has a countably infinite state space it is shown that the infinite mjls is stochastically stabilizable ss if and only if the associated countably infinite coupled lyapunov equations have a unique norm bounded strictly positive solution it is worth mentioning here that this result do not hold for mean square stabilizability mss since ss and mss are no longer equivalent in our set up see e g j baczynski optimal control for continuous time lq problems with infinite markov jump parameters ph d thesis federal university of rio de janeiro ufrj coppe 2000 to some extent a decomplexification technique and tools from operator theory in banach space and in particular from semigroup theory are the very technical underpinning of the paper

robust control design for nonlinear stochastic partial differential systems with poisson noise fuzzy implementation abstract this study addresses the robust h control design problem for nonlinear stochastic partial differential systems nspdss with poisson noise under the environment of random external disturbance in the spatio temporal domain for nspdss with poisson noise the robust h control design needs to solve a complex hamilton jacobi integral inequality hjii for robust control despite random external disturbance in general it is very difficult to solve the nonlinear partial differential hjii in order to simplify the design procedure a fuzzy stochastic partial differential system is proposed to approximate the nspds based on fuzzy interpolation approach then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semi discretization finite difference scheme and the kronecker product based on this model the robust h control design is proposed to achieve the robust control of nspdss via solving linear matrix inequalities lmis instead of an hjii the proposed robust fuzzy h controller has an efficient ability to attenuate the effect of spatio temporal external disturbance on the controlled output of nspdss from the area energy point of view finally a robust h control of the nervous system is given to confirm the control performance of the proposed robust control design method for nspdss with poisson noise

infinite markov jump bounded real lemma abstract a bounded real lemma is established providing an equivalent condition to stochastic stability ss of a continuous time infinite markovian jump linear system mjls with a prescribed l 2 stochastic disturbance attenuation level in terms of existence of solutions to an infinite set of coupled linear matrix inequalities lmis besides the interest in its own right the main result provides a fundamental tool for the development of an h like theory devoted to this class of systems

multiobjective investment policy for a nonlinear stochastic financial system a fuzzy approach the financial market always suffers from continuous and discontinuous jump changes and can be regarded as a nonlinear stochastic jump diffusion system most investors expect their investment policies to be not only higher benefits but also lower risk as a multiobjective optimization problem mop in this study a multiobjective h 2 h infty fuzzy investment is proposed for nonlinear stochastic jump diffusion financial systems to achieve the desired target with minimum investment cost and risk in pareto optimal sense simultaneously the takagi sugeno t s fuzzy model is used to approximate the nonlinear stochastic jump diffusion financial system to simplify the multiobjective h 2 h infty investment policy design procedure by the help of the t s fuzzy model the multiobjective h 2 h infty fuzzy investment policy problem of nonlinear stochastic financial system can be transformed to a linear matrix inequality constrained lmi constrained mop to avoid solving the annoying hamilton jacobi inequalities because the lmi constrained mop is not easy to directly calculate its pareto optimal solutions an indirect method is proposed to solve this mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems an lmi constrained multiobjective evolution algorithm lmi constrained moea is also developed to efficiently solve the pareto optimal solutions of the lmi constrained mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems when the pareto optimal regulation solutions are solved by the proposed lmi constrained moea investors can select one investment policy to achieve their desired target with minimum investment cost and risk according to his her own preference

on an infinite dimensional perturbed riccati differential equation arising in stochastic control existence and uniqueness of solutions for a class of infinite dimensional perturbed riccati differential equations in a certain banach space is our main concern in this paper besides the interest in its own right this class arises in control problems involving linear systems with countably infinite markov jump parameters

stabilization control for ito stochastic system with indefinite state and control weight costs in standard linear quadratic lq control the first step in investigating infinite horizon optimal control is to derive the stabilisation condition with the optimal lq controller this paper focus

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

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

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

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

systems of matrix rational differential equations arising in connection with linear stochastic systems with markovian jumping abstract in this paper a class of systems of matrix nonlinear differential equations containing as particular cases the systems of coupled riccati differential equations arising in connection with control of some linear stochastic systems is considered the system of differential equations considered in this paper are converted in a suitable nonlinear differential equation on a finite dimensional hilbert space adequately choosen this allows us to use the positivity properties of the linear evolution operator defined by the linear differential equations of lyapunov type our aim is to investigate properties of stabilizing and bounded solutions of the considered differential equations and to obtain some conditions ensuring the existence of such solutions conditions providing the existence of a maximal solution minimal solution respectively with respect to some classes of global solutions are presented it is shown that if the coefficients of the equations are periodic functions all these special solutions stabilizing maximal minimal are periodic functions too whenever possible the probabilistic arguments were avoided and so the results proved in the paper appear as results in the field of differential equations with interest in themselves

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

a bounded real lemma for jump systems this note presents a bounded real lemma for discrete time markovian jump linear systems mjlss we show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems for the case of one plant mode this condition reduces to the standard necessary and sufficient condition for discrete time systems we envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for mjlss

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

brief h control and filtering of discrete time stochastic systems with multiplicative noise linear discrete time systems with stochastic uncertainties in their state space matrices are considered the problems of finite horizon filtering and output feedback control are solved taking into account possible cross correlations between the uncertain parameters in both problems a cost function is defined which is the expected value of the relevant standard h performance index with respect to the uncertain parameters a solution to the filtering problem is obtained first by applying the adjoint system and deriving a bounded real lemma for this system this solution guarantees a prescribed estimation level of accuracy while minimizing an upper bound on the covariance of the estimation error the solution of the filtering problem is also extended to the infinite horizon case the results of the filtering problem are used to solve the corresponding output feedback problem a filtering example is given where a comparison is made with the results obtained using bounded uncertainty design techniques

static output feedback of state multiplicative systems with application to altitude control a linear parameter dependent approach for designing a constant output feedback controller for a linear time invariant system with stochastic multiplicative wiener type noise that achieves a minimum bound on either the stochastic h 2 or the h performance level is introduced a solution is achieved also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that corresponds to the vertices of the uncertainty polytope the stochastic uncertainties appear in both the dynamic and the measurement matrices of the system the problems are solved using the expected value of the standard performance index over the stochastic parameters the theory developed is applied to an altitude control example

obituary to a j pritchard on the 12th of august 2007 tony pritchard professor of mathematics at the university of warwick died suddenly at the age of 70 from a heart attack while on holiday with his family on the island of lanzarote both of the authors have had the privilege of working with him for many years we have lost both a colleague and a friend the following notes are dedicated to his memory

brief paper a unified design for state and output feedback h control of nonlinear stochastic markovian jump systems with state and disturbance dependent noise for a class of continuous time nonlinear stochastic markovian jump systems with state and disturbance dependent noise both the state and output feedback h control problems are studied based on the solvability of a set of coupled hamilton jacobi inequalities hjis we give a unified design for both state and dynamic output feedback h control via a common function u r t i e u x r t is a state feedback h control while u email protected r t is the desired output feedback h control

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

a character theory for projective representations of finite groups abstract in this paper we construct a character theory for projective representations of finite groups consequently we compute the number of distinct irreducible projective representations up to isomorphism of a finite group with a given associated schur multiplier and deduce properties on the degrees of such projective representations

the stability of stochastic coupled systems with time varying coupling and general topology structure we introduce a class of novel stochastic coupled systems in which the coupling structure is time varying and the topology structure is not strongly connected and first establish the system on a digraph with a time varying weight matrix motivated by du and li 2014 we give a hierarchical method to deal with digraphs without strong connectivity and establish the corresponding hierarchical algorithm to realize this approach also an example is given to illustrate our hierarchical algorithm and its feasibility in the sequel based on the theory of asymptotically autonomous systems kirchhoff s matrix tree theorem and lyapunov method several moment exponential stability criteria are presented including a lyapunov type theorem and a coefficient type criterion furthermore theoretical results are applied to stochastic coupled oscillators with time varying coupling structure sctcs and the stability criterion of sctcs is obtained finally the effectiveness of theoretical results is illustrated by two numerical examples

stochastic h sub spl infin tracking with preview for state multiplicative systems the problem of finite horizon h sub spl infin tracking for linear time varying systems with stochastic parameter uncertainties is investigated we consider three tracking patterns depending on the nature of the reference signal i e whether it is perfectly known in advance measured on line or previewed in a fixed time interval ahead the stochastic uncertainties appear in both the dynamic and measurement matrices of the system for each of the above three cases a game theory approach is applied for the state feedback case where given a specific reference signal the controller plays against nature which chooses the initial condition and the energy bounded disturbance the problems are solved using an expected value of the standard performance index over the stochastic parameters where necessary and sufficient conditions are found for the existence of a saddle point equilibrium the infinite horizon time invariant tracking problem is also solved the theory developed is demonstrated by a simple tracking example

stochastic stability analysis for 2 d roesser systems with multiplicative noise this paper is concerned with the robust stochastic stability analysis for two dimensional 2 d discrete state multiplicative noisy systems smnss in the roesser form we first derive a new sufficient condition under which linear discrete 2 d smnss are 2 d robustly stochastically stable the underlying problem can then be recast as a convex problem expressed by linear matrix inequalities which can be facilitated using existing numerical algorithms we then apply the obtained result to examine the 2 d robust stochastic stability for 2 d digital filters in the roesser form with random coefficient variation and saturation overflow arithmetic based on free weighting matrices and diagonally dominant matrices an illustrative example is presented to verify the usefulness and potential of the proposed results

predictor based control of stochastic systems with nonlinear diffusions and input delay abstract we consider the problem of state feedback control of linear continuous time stochastic systems with nonlinear diffusion terms affected by time varying input delays or equivalently by time varying state measurement delays we propose a finite dimensional control law based on closed loop predictors and derive sufficient delay bounds for the exponential stability in mean and exponential mean square stability with prescribed rate

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

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

filtering for discrete fuzzy stochastic systems with sensor nonlinearities this paper deals with the filtering problem for discrete time fuzzy stochastic systems with sensor nonlinearities there exist time varying parameter uncertainties and random noise depending on state and external disturbance the characteristic of nonlinear sensor is handled by a decomposition method by means of the parallel distributed compensation technique the design method of the robust h filter is presented sufficient conditions for the stochastic stability of the filtering error systems are derived such that the filter parameters can be explicitly obtained simulation results are given to illustrate the proposed method

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

jump linear quadratic gaussian control in continuous time the optimal quadratic control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes is addressed the systems are also subject to gaussian input and measurement noise the optimal solution for the jump linear quadratic gaussian jlqc problem is given this solution is based on a separation theorem the optimal state estimator is sample path dependent if the plant parameters are constant in each value of the underlying jumping process then the controller portion of the compensator converges to a time invariant control law however the filter portion of the optimal infinite time horizon jlqc compensator is not time invariant thus a suboptimal filter which does converge to a steady state solution under certain conditions is derived and a time invariant compensator is obtained

defending against strategic manipulation in uninorm based multi agent decision making abstract we consider the problem of multi agent group decision making we describe the possible use of the uninorm aggregation operator as a way of combining individual agents preference functions to obtain a group preference function we then discuss the possibility of an agent using a type of strategic manipulation of the preference information it provides in order to get the group to select its most preferred alternative a mechanism is then suggested for modifying the construction of the group decision function to defend against this type of strategic manipulation in addition to considering the case where the preference information is provided numerically we consider the case of ordinal preference information

penalizing strategic preference manipulation in multi agent decision making we consider the problem of group decision making where the selection process is based upon a group preference function obtained by an aggregation of the participating agents individual preference functions we describe some methods for formulating the group preference from the individual preference functions we note the possibility of the individual agents strategically manipulating the information they provide so as to further their own goal of getting their most preferred alternative selected by the group with this in mind we suggest ways of modifying the formulation of the group decision functions to discourage strategic manipulation by the participating agents

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

brief paper almost sure exponential stabilisation of stochastic systems by state feedback control so far a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability this paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean square sense the results are expressed in terms of linear matrix inequalities lmis which are easy to be checked in practice by using matlab toolbox moreover the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

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

numerical solution of stochastic nash games with state dependent noise for weakly coupled large scale systems abstract this paper discusses the infinite horizon stochastic nash games with state dependent noise after establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross coupled stochastic algebraic riccati equations csares a new algorithm that combines newton s method with two fixed point algorithms for solving the csares is derived as a result it is shown that the proposed algorithm attains quadratic convergence and the reduced order computations for sufficiently small parameter e as another important feature the high order approximate strategy that is based on the iterative solutions is proposed using such strategy the degradation of the cost functional is investigated finally in order to demonstrate the efficiency of the proposed algorithms computational examples are provided

on twisted group frames abstract in this paper we study g frames for finite dimensional hilbert spaces where g is a finite group and is a unitary schur multiplier of g we apply the characterizations for tight g frames and central g frames to investigation of g frames that have the maximal spanning property we apply the theory of twisted group frames to obtain a criterion for maximal spanning vectors that generalizes the main result of 16 theorem 1 7 moreover we prove that a projective representation does not admit any maximal spanning vector if it has an at least 2 dimensional subrepresentation that is equivalent to a central projection induced subrepresentation of the regular representation

on a partially observable lqg problem for systems with markovian jumping parameters in this paper a variant of the lqg problem for systems with markovian jumping parameters is studied it is assumed that the system is partially observable in the sense that we do not have access to the jumping parameter via nonlinear filtering the problem is recast as one with complete information it is then shown that a certain averaged control is an optimal policy vis a vis a modified quadratic cost apart from its intrinsic theoretical interest this result has an important bearing on a number of different analyses related with the original quadratic cost

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

on a class of rational matrix differential equations arising in stochastic control we prove a monotonicity and a comparison theorem for the solutions of a rational matrix differential equation appearing in stochastic control and derive existence and convergence results for the solutions of this differential equation moreover in the time invariant case we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing solution

robust h control with maximal decay rate for linear discrete time stochastic systems abstract the problems of robust stabilization and robust h control with maximal decay rate are investigated for discrete time stochastic systems with time varying norm bounded parameter uncertainties for the robust stabilization problem an optimal state feedback controller is designed which ensures that the closed loop system is robustly stochastically stable with maximal decay rate while for the robust h control problem the designed state feedback controller guarantees that the resulting closed loop system is with a specified h performance level besides robust stochastic stability with maximal decay rate the method based on the convex optimization and linear matrix inequality is developed to solve these problems two examples are provided to show the effectiveness of the proposed approach

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective

linear moving horizon estimation with pre estimating observer in this note a moving horizon estimation mhe strategy for detectable linear systems is proposed like the idea of pre stabilizing model predictive control the states are estimated by a forward simulation with a pre estimating observer in the mhe formulation compared with standard linear mhe approaches it has more degrees of freedom to optimize the noise filtering tuning parameters are chosen to minimize the effects of measurement noise and model errors which is implemented by finding tightest estimation error bounds the performance of the proposed observer is demonstrated on one linear discrete time example