Observer-Based Finite-Time H∞ Control of Singular Markovian Jump Systems

Abstract EN

This paper addresses the problem of finite-time H∞ control via observer-based state feedback for a family ofsingular Markovian jump systems (SMJSs) with time-varying norm-bounded disturbance.

Firstly, the concepts ofsingular stochastic finite-time boundedness and singular stochastic finite-time H∞ stabilization via observer-basedstate feedback are given.

Then an observer-based state feedback controller is designed to ensure singular stochasticfinite-time H∞ stabilization via observer-based state feedback of the resulting closed-loop error dynamic SMJS.

Sufficient criteria are presented for the solvability of the problem, which can be reduced to a feasibility probleminvolving linear matrix inequalities with a fixed parameter.

As an auxiliary result, we also discuss the problemof finite-time stabilization via observer-based state feedback of a class of SMJSs and give sufficient conditions ofsingular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs.

Finally, illustrativeexamples are given to demonstrate the validity of the proposed techniques.