Finite-Time Control for Markovian Jump Systems with Polytopic Uncertain Transition Description and Actuator Saturation

Abstract

The problem of finite-time $L_2\text{-}{L}_{\infty }$ control for Markovian jump systems (MJS) is investigated. The systems considered time-varying delays, actuator saturation, and polytopic uncertain transition description. The purpose of this paper is to design a state feedback controller such that the system is finite-time bounded (FTB) and a prescribed $L_2\text{-}{L}_{\infty }$ disturbance attenuation level during a specified time interval is guaranteed. Based on the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design the delayed feedback controller which satisfies the given attenuation level. Finally, illustrative examples show that the proposed conditions are effective for the design of robust state feedback controller.