Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities

Author:

Guo Xinye1,Li Yan2ORCID,Liu Xikui13ORCID

Affiliation:

1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

2. Department of Fundamental Courses, Shandong University of Science and Technology, Jinan 250031, China

3. Department of Electrical Engineering and Information Technology, Shandong University of Science and Technology, Jinan 250031, China

Abstract

This paper concentrates on the finite-time H∞ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) H∞ state feedback controller and an SFT H∞ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov–Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT H∞ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.

Funder

National Natural Science Foundation of China

Shandong Provincial Natural Science Foundation

Publisher

MDPI AG

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