Finite-TimeH∞Control for a Class of Discrete-Time Markov Jump Systems with Actuator Saturation via Dynamic Antiwindup Design

Abstract

We deal with the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. A controller designed for unconstrained systems combined with a dynamic antiwindup compensator is given to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. The proposed conditions allow us to find dynamic anti-windup compensator which stabilize the closed-loop systems in the finite-time sense. All these conditions can be expressed in the form of linear matrix inequalities and therefore are numerically tractable, as shown in the example included in the paper.

An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

“…Recently, some investigations are carried out on the MJSs with actuator saturation [37][38][39][40][41][42][43][44][45][46]. By applying appropriate Lyapunov functions, robust H ∞ controller for uncertain discrete-time MJSs is design to guarantee the stochastic stability of the corresponding closed-loop systems in [39].…”

“…Finite-time H ∞ control for a class of discrete-time Markov jump systems with actuator saturation was probed via dynamic anti-windup design in [46]. Most recently, under the actuator saturation and partly known transition probabilities, the corresponding results for anti-windup design of uncertain Markovian jump systems are presented in [47][48][49].…”

“…Compared with the existing results in [45,46,47,48], we investigate a class of Markovian jump continuous-time singular systems even with a standard Wiener process, not Markovian jump discrete-time systems. Compared with the existing results in [43,44,50], we introduce the general unknown transition rates for the Markov process, which is more general than the partly accessible transition rates.…”