Improved Non-Fragile State Feedback Control for Stochastic Jump Systems With Uncertain Parameters and Mode-Dependent Time-Varying Delays

Kun Ma,Guowei Zhao,Yuqian Lin,Guangming Zhuang,Huasheng Zhang,Jie Wang

doi:10.1109/access.2020.2996756

Abstract

This paper reports the investigation on non-fragile state feedback control for stochastic Markovian jump systems with uncertain parameters and mode-dependent time-varying delays. The resulted closed-loop system is stochastic stabilization by virtue of an improved L-K functional. By free-weight-matrix technique, the non-fragile state feedback controller is designed and novel conditions for robust stochastic stabilization are acquired in the form of linear matrix inequalities. Two examples including a take-off and landing guidance system are employed to show the effectiveness and validity of the proposed approach.

Highlights

As a very significant type of hybrid systems, Markovian jump systems (MJSs) have been paid more and more concern for many years
Non-fragile controller was discussed for repeated scalar non-linearities time-varying delays systems in [51]; non-fragile stochastic stabilization for uncertain stochastic time-delay systems with time-dependent parameters was solved in [52]; non-fragile stabilization for MJSs were considered in [53]–[57]; nonfragile H∞ state feedback controller was mentioned for singular fuzzy MJS with a interval delay in [58]
This paper has reported the investigation on non-fragile control for stochastic MJSs with uncertain parameters and mode-dependent time-varying delays

Summary

INTRODUCTION

As a very significant type of hybrid systems, Markovian jump systems (MJSs) have been paid more and more concern for many years. Non-fragile controller was discussed for repeated scalar non-linearities time-varying delays systems in [51]; non-fragile stochastic stabilization for uncertain stochastic time-delay systems with time-dependent parameters was solved in [52]; non-fragile stabilization for MJSs were considered in [53]–[57]; nonfragile H∞ state feedback controller was mentioned for singular fuzzy MJS with a interval delay in [58]. According to our limited knowledge, the issue of non-fragile control for stochastic MJSs with uncertain parameters and mode-dependent time-varying delays is rarely studied, which stimulates the current research. This paper will address the issue of the non-fragile state feedback controller for stochastic MJSs with uncertain parameters and time-varying mode-dependent delays. (3) non-fragile controller is considered and improved mode-dependent and delay-dependent L-K functional is constructed in this paper. E(·) represents the expectation operator; | · | represents the Euclidean vector norm; Matrix Q > 0(Q ≥ 0) refers to Q is positive definite( positive semidefinite ). ∗ expresses a term that is induced by symmetry in symmetric block matrices or long matrix expressions

PROBLEM FORMULATION AND PRELIMINARIES

SIMULATION EXAMPLES

CONCLUSION