On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulatio

Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.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.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor G. Chesi

Stabilisation of descriptor Markovian jump systems with partially unknown transition probabilities

This paper is concerned with the stability and stabilisation problems for continuous-time descriptor Markovian jump systems with partially unknown transition probabilities. In terms of a set of coupled linear matrix inequalities (LMIs), a necessary and sufficient condition is firstly proposed, which ensures the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding necessary and sufficient condition on the existence of a mode-dependent state-feedback controller, which guarantees the closed-loop systems stochastically admissible by employing the LMI technique, is derived; the stabilizing state-feedback gain can also be expressed via solutions of the LMIs. Finally, numerical examples are given to demonstrate the validity of the proposed methods

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional-derivative control strategy is presented, where the derivative gain is to make the closed-loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods

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 diusion part of the underlying stochastic system

Stability Analysis of Continuous-Time Switched Systems with a Random Switching Signal

This paper 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.Comment: 6 pages, 6 figures, accepted by IEEE-TA

Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case