Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems

Feng Zhao,Jinde Cao,Jianlong Qiu,Xiangyong Chen,Ming Guo

doi:10.15388/namc.2020.25.20654

Abstract

This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.

Highlights

Singular systems can naturally describe the real systems than regular systems because of the fact that singular systems can better preserve the structure of some physical systems and impulsive elements [5, 9, 13, 22, 23, 30]
Based on the views above, this paper focuses on the observer-based control problem for a class of stochastic singular nonlinear systems with Itô-type stochastic disturbance
Based on the sufficient conditions, the observer-based control technique has been proposed for a class of stochastic singular nonlinear systems, where the control gain and observer gain can be obtained by solving linear matrix inequalities

Summary

Introduction

Singular systems can naturally describe the real systems than regular systems because of the fact that singular systems can better preserve the structure of some physical systems and impulsive elements [5, 9, 13, 22, 23, 30]. The problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems was investigated in [38]. In [1], the finite-time stochastic input-to-state stability problem for a class of impulsive switched stochastic nonlinear systems was investigate. In [42], the problems of finite-time globally asymptotical stability in probability and finite-time stochastic input-to-state stability for switched stochastic nonlinear systems were investigated. Based on the views above, this paper focuses on the observer-based control problem for a class of stochastic singular nonlinear systems with Itô-type stochastic disturbance. A new design method is proposed to design the controller gain and observer gain of the observer-based controller for a class of stochastic singular nonlinear systems by solving linear matrix inequalities.

Problem formulation

Main results

Simulation examples

Conclusions