output feedback h_ infty control of continuous time infinite markovian jump linear systems via lmi methods the output feedback h infty control is addressed for a class of continuous time markov jump linear systems with the markov process taking values in an infinite countable set mathcal s we consider that only an output and the jump parameters are available to the controller via a certain bounded real lemma together with some extensions of schur complements and of the projection lemma a theorem which characterizes whether there exists a full order solution to the disturbance attenuation problem is devised in terms of two different linear matrix inequality lmi feasibility problems this result connects a certain projection approach to an lmi problem which is more amenable to computer solution and hence for design we conclude the paper with some design algorithms for the construction of such controllers and an illustrative example

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

infinite horizon stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper studies the infinite horizon mixed h 2 h control for discrete time stochastic systems with state and disturbance dependent noise we shall first establish a version of stochastic bounded real lemma sbrl which by itself has theoretical importance based on the sbrl it is shown that under the condition of exact observability the existence of a static state feedback h 2 h controller is equivalent to the solvability of four coupled matrix valued equations a suboptimal h 2 h controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix valued equations

stochastic stability of jump linear systems in this note some testable conditions for mean square i e second moment stability for discrete time jump linear systems with time homogenous and time inhomogenous finite state markov chain form processes are presented

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

a technique for realizing linear phase iir filters a real time iir filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional fir filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay iir filters this structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real time recursive implementation of the noncausal transfer function h z sup 1 the time reversed section technique used to realize exactly linear phase iir filters is described the effects of finite section length on the sectional convolution are analyzed a simulation methodology is developed to address the special requirements of simulating a time reversed section filter a design example is presented with computer simulation to illustrate performance in terms of overall magnitude response and phase linearity as a function of finite section length nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct fir implementation

mean square stability for discrete bounded linear systems in hilbert space the asymptotic behaviour for infinite dimensional discrete linear systems driven by white noise is considered in this paper both the evolution and convergence of the state correlation operators sequence are analysed mean square stability conditions are investigated including a comparison with the deterministic stability problem the particular case of compact operators is considered in some detail

some windows with very good sidelobe behavior some of the windows presented by harris 1 are not correct in terms of their reported peak sidelobes and optimal behavior we present corrected plots of harris windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints the temporal weightings are characterized as a sum of weighted cosines over a finite duration the plots enable the reader to select a window to suit his requirements in terms of bias due to nearby sidelobes and bias due to distant sidelobes

robust h infinity control in the presence of stochastic uncertainty this paper considers a robust h infinity state feedback control problem for linear uncertain systems with stochastic uncertainty the uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint a state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties

asymptotic properties of input output operators norm associated with singularly perturbed systems with multiplicative white noise in this paper we study the problem of the asymptotic property of the norm of input output operators related to a class of singularly perturbed stochastic linear systems the system is under perturbation of multiplicative white noise by using reduction order and boundary layer techniques it is shown that the norm of the operator of the perturbed system is less than a given number gamma when the small perturbation varepsilon tends to zero if both the related norms of the reduced subsystem and the boundary layer subsystem are less than gamma furthermore a stabilizing robust controller is designed which is independent of perturbation varepsilon

optimum binary windows for discrete fourier transforms a class of windows called binary windows for the frequency domain implementation of the discrete fourier transform is proposed while the conventional time domain windowing requires n 2 stored values of the data window and n multiplications the binary windows do not require multiplications or stored constants rather they are replaced by shift and add operations typical hardware structures are presented for efficient implementation of the binary windows

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

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

quadratic control with partial information for discrete time jump systems with the markov chain in a general borel space this paper deals with the finite horizon quadratic optimal control problem of discrete time markov jump linear systems mjls considering the case in which the markov chain takes values in a general borel space s it is assumed that the controller has access to an output variable as well as the jump parameter the goal is to design a dynamic markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time it is shown that an optimal controller can be obtained from two s coupled difference riccati equations one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available by s coupled it is meant that the difference riccati equations are coupled via an integral over s this result which can be seen as a separation principle for discrete time mjls generalizes previous ones that were restricted to the markov chain taking values in a finite set

brief paper stabilization of markovian jump linear system over networks with random communication delay this paper is concerned with the stabilization problem for a networked control system with markovian characterization we consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a markov chain the resulting closed loop system is modeled as a markovian jump linear system with two jumping parameters and a necessary and sufficient condition on the existence of stabilizing controllers is established an iterative linear matrix inequality lmi approach is employed to calculate a mode dependent solution finally a numerical example is given to illustrate the effectiveness of the proposed design method

mathcal h_ infty control for 2 d markov jump systems in roesser model this paper considers the problem of asynchronous mathcal h infty control for two dimensional 2 d markov jump systems the underlying system is described based upon the roesser model especially the hidden markov model is employed when dealing with the asynchronization between a controlled system and a controller and the relation between them is constructed through a conditional probability matrix based on the lyapunov function technique the asymptotic mean square stability and mathcal h infty noise attenuation performance are investigated for the closed loop 2 d system moreover the controller gain can be obtained by solving a convex optimization problem an example is presented to show the effectiveness and potential of the proposed new design technique

discrete time mean field stochastic linear quadratic optimal control problems this paper firstly presents necessary and sufficient conditions for the solvability of discrete time mean field stochastic linear quadratic optimal control problems secondly the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method thirdly by introducing several sequences of bounded linear operators the problem is formulated as an operator stochastic linear quadratic optimal control problem by the kernel range decomposition representation of the expectation operator and its pseudo inverse the optimal control is derived using solutions to two algebraic riccati difference equations finally by completing the square the two riccati equations and the optimal control are also obtained

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 in max product and max plus systems with markovian jumps we study max product and max plus systems with markovian jumps and focus on stochastic stability problems at first a lyapunov function is derived for the asymptotically stable deterministic max product systems this lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of max product systems with markovian jumps many step lyapunov functions are then used to derive necessary and sufficient conditions for stochastic stability the results for the max product systems are then applied to max plus systems with markovian jumps using an isomorphism and almost sure bounds for the asymptotic behavior of the state are obtained a numerical example illustrating the application of the stability results on a production system is also given

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

stochastic stabilization of hybrid differential equations this paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system new methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization by stochastic feedback controls two types of structure controls namely state feedback and output injection are discussed our stabilization criteria are in terms of linear matrix inequalities lmis whence the feedback controls can be designed more easily in practice a couple of examples and computer simulations are worked out to illustrate our theory

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

finite horizon h_ 2 h_ infty control for discrete time stochastic systems with markovian jumps and multiplicative noise in this note we consider the finite horizon mixed h 2 h control problem for discrete time stochastic linear systems subject to markov jump parameters and multiplicative noise firstly we derive a stochastic bounded real lemma sbrl which is used to establish a necessary and sufficient condition for the existence of the mixed h 2 h control via the solvability of four coupled difference matrix valued recursions cdmrs moreover a state feedback h 2 h controller is designed by means of the solutions of cdmrs

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

mackey functors with chain conditions abstract letabe a green functor for a finite groupgand letmbe a lefta module mis callednoetherian artinian if the lattice of all submodules ofmsatisfies acc respectively dcc mis calledtotally noetherian totally artinian ifmxis noetherian respectively artinian for every finiteg setx in this paper it is shown that the totally noetherian totally artinian lefta modules behave in the same way as the classical noetherian artinian modules the left noetherian left artinian green functors are less well behaved but some properties from classical algebra still hold it is shown that cohen s theorem holds in this setting our main result shows that if a commutative green functorais artinian then the ringsa h jac a h are semisimple artinian for all subgroupshofg

exponential stabilization of a class of stochastic system with markovian jump parameters and mode dependent mixed time delays in this technical note the globally exponential stabilization problem is investigated for a general class of stochastic systems with both markovian jumping parameters and mixed time delays the mixed mode dependent time delays consist of both discrete and distributed delays we aim to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense first by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem then a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality lmi approach finally it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of lmis numerical simulation is carried out to demonstrate the effectiveness of the proposed methods

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

markowitz s mean variance portfolio selection with regime switching from discrete time models to their continuous time limits we study a discrete time version of markowitz s mean variance portfolio selection problem where the market parameters depend on the market mode regime that jumps among a finite number of states the random regime switching is delineated by a finite state markov chain based on which a discrete time markov modulated portfolio selection model is presented such models either arise from multiperiod portfolio selections or result from numerical solution of continuous time problems the natural connections between discrete time models and their continuous time counterpart are revealed since the markov chain frequently has a large state space to reduce the complexity an aggregated process with smaller state space is introduced and the underlying portfolio selection is formulated as a two time scale problem we prove that the process of interest yields a switching diffusion limit using weak convergence methods next based on the optimal control of the limit process obtained from our recent work we devise portfolio selection strategies for the original problem and demonstrate their asymptotic optimality

dissipativity based asynchronous filtering for periodic markov jump systems abstract this paper is devoted to developing a periodic and asynchronous filter for periodic markov jump systems a periodic and asynchronous filter means that the filter parameters are s periodic for a given operating mode and its operating modes are unnecessary to be identical but form a periodic hidden markov model together with the modes of the plant a sufficient condition is proposed to guarantee that the filtering error system is exponentially mean square stable and strictly q s r dissipative to realize this filter a slack matrix is introduced to deal with the nonlinearity and finsler s lemma is applied such that the decision variables are reduced finally a numerical simulation provides verification for the effectiveness of our designed filter

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

mixed control the discrete time case abstract a stochastic h and a mixed stochastic h 2 h control problem for discrete time systems are considered and solved conditions for existence of a solution are derived based on the solvability of an equivalent minimax problem in this framework it is possible to consider at the same time both stochastic and deterministic disturbances highlighting their mutual effects the controller can be designed by solving a system of three coupled riccati equations such equations display how the h 2 type minimization problem and the h type constraint influence each other

infinite horizon h2 h control for discrete time time varying markov jump systems with multiplicative noise in this paper we consider the infinite horizon h 2 h control problem for discrete time time varying linear systems subject to markov jump parameters and state multiplicative noise a stochastic version of a bounded real lemma is firstly developed for a general class of discrete time time varying markov jump systems with state and disturbance multiplicative noise by which we present a necessary and sufficient condition for the solvability of the h 2 h control problem in terms of four coupled discrete time riccati equations moreover the obtained design is applied to a macroeconomic problem to verify its effectiveness

stability analysis of continuous time switched systems with a random switching signal this technical note is concerned with the stability analysis of continuous time switched systems with a random switching signal the switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part the stochastic stability of such switched systems is studied using a lyapunov approach a necessary and sufficient condition is established in terms of linear matrix inequalities the effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition

technical communique h output feedback control of discrete time systems with state multiplicative noise linear discrete time systems with stochastic uncertainties in their state space model are considered the problem of dynamic output feedback control is solved via a new approach for both the finite horizon and the stationary cases in both cases a cost function is defined which is the expected value of the standard h performance index with respect to the uncertain parameters an example is given which demonstrates the applicability of the theory

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

on eigenvalue sets and convergence rate of ito stochastic systems with markovian switching this technical note is concerned with stability analysis and stabilization of ito stochastic systems with markovian switching a couple of eigenvalue sets for some positive operator associated with the stochastic system under study are defined to characterize its stability in the mean square sense properties for these eigenvalue sets are established based on which we show that the spectral abscissa of these eigenvalues sets are the same and thus these eigenvalue sets are equivalent in the sense of characterizing the stability of the system also it is shown that the guaranteed convergence rate of the markovian jump ito stochastic systems can be determined by some eigenvalue set finally a linear matrix inequality based approach is proposed to design controllers such that the closed loop system has guaranteed convergence rate some numerical examples are carried out to illustrate the effectiveness of the proposed approach the research in this technical note opens several perspectives for future work stated as some open problems

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

adaptive tracking for stochastic nonlinear systems with markovian switching the problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary markovian switching is considered in this note an ito formula is proposed for stochastic integral equations with an integral about martingale measure an adaptive backstepping controller is designed such that the closed loop system has a unique solution that is globally bounded in probability and l4 norm of the tracking error converges to an arbitrarily small neighborhood of zero a simulation example demonstrates the efficiency of the proposed scheme

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

filtering s coupled algebraic riccati equations for discrete time markov jump systems abstract this paper deals with a set of s coupled algebraic riccati equations that arises in the study of filtering of discrete time linear jump systems with the markov chain in a general borel space s by s coupled it is meant that the algebraic riccati equations are coupled via an integral over s conditions for the existence and uniqueness of a positive semi definite solution to the filtering s coupled algebraic riccati equations are obtained in terms of the concepts of stochastic detectability and stochastic stabilizability this result is then applied to solve the infinite horizon minimum mean square linear markov jump filtering problem the obtained results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite state space

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

state estimation for asynchronous sensor systems with markov jumps and multiplicative noises abstract this paper is concerned with the asynchronous state estimation problem for sensor systems subject to markov jump parameters and multiplicative noises the asynchronous sensors considered can have arbitrary sampling rates and arbitrary initial sampling instants by transforming the asynchronous measurements within each fusion interval into an augmented measurement the equivalent measurement equation and state equation at the fusion time instant are constructed based on the two equations a linear minimum mean squared error lmmse estimator is developed using the orthogonality projection principle due to the existence of the common process noise in the equivalent process and measurement noises the equivalent process and measurement noises are cross correlated and the equivalent measurement noises are autocorrelated these correlations are taken into account in the estimator design the stationary case is also studied and the sufficient condition is established for the stability of the proposed estimator a target tracking example is provided to illustrate the effectiveness of the proposed estimator

on stability and lq control of mjls with a markov chain with general state space we study the mean square stability and the lq control of discrete time markov jump linear systems where the markov chain has a general state space the mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a lyapunov equation and a uniformity result respectively an algorithm for testing the mean square stability is also developed based on the uniformity result the finite and infinite horizon lq problems are considered and their solutions are characterized by appropriate riccati integral equations an application to networked control systems ncs is finally presented and a simple example is studied via simulation

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

almost sure estimation and synthesis of ultimate bounds for discrete time markov jump linear systems this paper is concerned with the problems of almost sure ultimate bound estimation and controller design for markov jump linear systems with bounded stochastic disturbances by utilising a lyapunov based scheme proposed in this paper an almost sure estimation of ellipsoidal ultimate bound eub of the system is obtained through tractable matrix inequalities on the basis of the estimation results the problem of designing mode dependent state feedback controllers that make the closed loop system admit a prescribed ellipsoid as an eub is considered the obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information finally a practical example in dc motor devices is presented to demonstrate the applicability of the obtained results

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

lq optimal sampled data control under stochastic delays gridding approach for stabilizability and detectability we solve a linear quadratic optimal control problem for sampled data systems with stochastic delays the delays are stochastically determined by the last few delays the proposed optimal controller

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

fir filter design over a discrete powers of two coefficient space fir digital filters with discrete coefficient values selected from the powers of two coefficient space are designed using the methods of integer programming the frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients both the weighted minimax and the weighted least square error criteria are considered using a weighted least square error criterion it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding

the linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and markovian jumping in this paper the linear quadratic optimization problem for a class of linear stochastic systems subject both to multiplicative white noise and markovian jumping is investigated two classes of admissible controls are considered one of these classes contains controls with additional property that corresponding trajectories tend to zero in mean square when tends to spl infin while concerning the controls contained in the second class of admissible controls there is not any stability assumption in the optimization problem over the first class of admissible controls the cost functional could have indefinite sign of weights matrices an iterative procedure to compute the maximal solution of the systems of generalized riccati equations is provided a numerical example to illustrate the applicability of the iterative procedure is given

lq control of discrete time jump systems with markov chain in a general borel space in this technical note it is studied the lq optimal control problem for discrete time markov jump linear systems considering the case in which the markov chain takes values in a general borel space cal m it is shown that the solution of the lq optimal control problem is obtained in terms of the positive semi definite solution s ell ell in cal m of cal m coupled algebraic riccati equations by cal m coupled we mean that the algebraic riccati equations are coupled via an integral over a transition probability kernel cal g cdot vert cdot having a density g cdot vert cdot with respect to a sigma finite measure mu on cal m it is obtained sufficient conditions based on the concept of stochastic stabilizability and stochastic detectability for the existence and uniqueness of this positive semi definite solution these results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

stationary filter for continuous time markovian jump linear systems we derive a stationary filter for the best linear mean square filter blmsf of continuous time markovian jump linear systems mjls it amounts here to obtain the convergence of the error covariance matrix of the blmsf to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain theta t it is shown that there exists a unique solution for the stationary riccati filter equation and this solution is the limit of the error covariance matrix of the blmsf the advantage of this scheme is that it is easy to implement since the filter gain can be performed offline leading to a linear time invariant filter

lq nash games with random entrance an infinite horizon major player and minor players of finite horizons we study dynamic games with randomly entering players staying in the game for different lengths of time particularly a class of discrete time linear quadratic lq games involving a major player who has an infinite time horizon and a random number of minor players is considered the number of the new minor players entering at some instant of time is random and it is described by a markov chain the problem of the characterization of a nash equilibrium consisting of linear feedback strategies is reformulated as a set of coupled finite and infinite horizon lq optimal control problems for markov jump linear systems mjls sufficient conditions characterizing nash equilibrium are then derived the problem of games involving a large number of minor players is then addressed using a mean field mf approach and asymptotic varepsilon nash equilibrium results are derived sufficient conditions for the existence of a mf nash equilibrium are finally stated

indefinite quadratic with linear costs optimal control of markov jump with multiplicative noise systems in this paper we consider the stochastic optimal control problem of discrete time markov jump with multiplicative noise linear systems the performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables the weighting matrices of the state and control for the quadratic part are allowed to be indefinite we present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized riccati difference equations interconnected with a set of coupled linear recursive equations for the case in which the quadratic term matrices are non negative this necessary and sufficient condition can be written in a more explicit way the results are applied to a problem of portfolio optimization

defect theory for maximal ideals and simple functors keywords green functor source green correspondence maximal ideal finite group fixed point algebra defect theory for g algebras defect group restriction transfer conjugation defect pair functorial ideal simple g functors reference ctg article 1991 002doi 10 1016 0021 8693 91 90168 8 record created on 2008 12 16 modified on 2017 05 12