Observer Design for Delayed Markovian Jump Systems with Output State Saturation

Guoliang Wang,Bo Feng

doi:10.1155/2018/9572927

Abstract

This paper considers the observer design problem of continuous-time delayed Markovian jump systems with output state saturation. Different from the traditionally observer-based saturation control methods, a kind of system output state saturation with a partially delay-dependent property is proposed, where both nondelay and delay states exist at the same time but happen asynchronously. By exploiting the Bernoulli variable, the probability distributions of such two states are described and considered in the observer design. Based on an improved equality applied to deal with saturation terms, sufficient conditions for the designed observer with three kinds of output saturations are all provided with LMI forms. Finally, a numerical example is given to indicate the effectiveness of the obtained results.

Highlights

As we know, Markovian jump system (MJS) is a special kind of stochastic hybrid dynamical systems
This paper considers the observer design problem of continuous-time delayed Markovian jump systems with output state saturation
In the modern control theory, it is obvious that the state feedback control has advantages in solving the problems of system stability, pole placement, stabilization, and optimal control

Summary

Introduction

Markovian jump system (MJS) is a special kind of stochastic hybrid dynamical systems. Some results were presented in [37, 38] By investigating these references, it is found that there are still many problems to be considered. The observer design problem of continuoustime delayed Markovian jump systems with output state saturation is studied, where the output state saturation is partially delay-dependent. The main contributions of this paper are generalized as follows: (1) A kind of observer based on partially delay-dependent output is proposed. Both nondelay and delay states are contained in output saturation simultaneously, but their occurrences are asynchronous. (3) Sufficient conditions of the designed observer are obtained by applying an improved inequality to deal with the saturation terms. We use “∗” as an ellipsis for the terms induced by symmetry, diag{⋅ ⋅ ⋅ } for a block-diagonal matrix, and (M)⋆ ≜ M + MT

Problem Formulation

Main Results

Numerical Examples

Conclusion