Wenhai Qi

Controller design for time-delay system with stochastic disturbance and actuator saturation via a new criterion

Abstract This paper deals with the problem of controller design for time-delay system with stochastic disturbance and actuator saturation. By use of more appropriate Lyapunov–Krasovskii functional (LKF) and a new criterion for the domain of attraction, less conservative conditions for stochastic stability are proposed. Then, the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome. These sufficient conditions are derived in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the given results.

Exponential stability and L1-gain analysis for positive time-delay Markovian jump systems with switching transition rates subject to average dwell time

Abstract The paper deals with the problems of exponential stability and L 1 -gain analysis for positive time-delay Markovian jump systems (MJSs) with switching transition rates. Another set of useful regime-switching model is given, which extends fixed transition rates to time-varying transition rates. By resorting to the linear co-positive Lyapunov function and average dwell time, sufficient conditions for exponential stability are proposed in terms of standard linear programming. Based on the obtained results, L 1 -gain performance is analyzed. Finally, an example is proposed to illustrate the validity of the main results.

Further results on finite-time stabilisation for stochastic Markovian jump systems with time-varying delay

ABSTRACT In this paper, we study the issue of finite-time stabilisation for stochastic Markovian jump systems with time-varying delay by considering a new criterion on finite-time stability. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying the finite-time stability of the plant as well as controller synthesis are established in standard linear matrix inequalities. The practical example about a single-link robot arm model demonstrates the validity of the main results.

Stability analysis and control synthesis for positive semi-Markov jump systems with time-varying delay

Abstract This paper deals with stability analysis and control synthesis for positive semi-Markov jump systems (S-MJSs) with time-varying delay, in which the stochastic semi-Markov process related to nonexponential distribution is considered. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing have some conservation. To deal with these problems, the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition. Then, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear Lyapunov–Krasovskii functional depending on the bound of time-varying delay. Furthermore, an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable in standard linear programming. The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs with time-varying delay under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, three examples, one of which is the virus mutation treatment model, are given to demonstrate the validity of the main results.

Disturbance-observer-based control for time-delay Markovian jump systems subject to actuator saturation

This paper is concerned with disturbance-observer-based control for Markovian jump systems with time delay and actuator saturation. By virtue of the disturbance-observer-based control technique and an appropriate mode-dependent Lyapunov–Krasovskii functional, an anti-disturbance controller is designed to ensure that the resulting closed-loop systems are stochastically stable, as well as estimation of the domain of attraction. Furthermore, an iterative optimization method is proposed to acquire the maximum estimate of the domain of attraction by solving a set of linear matrix inequalities. Finally, a simulation illustrates the effectiveness of the proposed schemes.

Controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation

ABSTRACT The paper deals with controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation by implying a new criterion for the domain of attraction firstly. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying stochastic stability of the plant are established. Then, the state feedback controller is designed to expand the domain of attraction of the corresponding closed-loop system. The procedure of deriving controller gain matrices is converted into an optimisation problem with constraints of a set of linear matrix inequalities. The mathematical model of RLC series circuit illustrates the validity of the obtained results.

L1 finite-time stabilization for positive semi-Markovian switching systems

Abstract This paper investigates robust finite-time stabilization scheme for positive semi-Markovian switching systems (S-MSSs). Semi-Markovian process (SMP), external disturbances, and transient performances at a finite-time level may appear in a controlled system. A more general system model for S-MSSs that covers Markovian switching systems (MSSs) as a special case is suitable for describing some complex systems that are subject to random abrupt changes in structure and parameter. The main motivation for this is that finite-time problems can be used to describe the transient performance of practical industrial control processes. First, under the framework of stochastic semi-Markovian Lyapunov functions theory, some sufficient conditions for finite-time boundedness (FTBs) and L 1 FTBs criteria for positive S-MSSs are proposed for all admissible disturbances. Then, a novel L 1 finite-time controller design method that employs the gain matrix decomposition method is presented to reduce some conservativeness, thereby guaranteeing that the resulting closed-loop system (RLCS) could achieve positivity, FTBs, and attain a prescribed L 1 noise attenuation performance index in standard linear programming (LP). Finally, a practical example is introduced to show the effectiveness of the main theory