Disturbance Observer-Based Input-Output Finite-Time Control of a Class of Nonlinear Systems

Leipo Liu,Shuzhong Song,Zhumu Fu,Xiaona Song

doi:10.1155/2017/7202584

Abstract

This paper is concerned with disturbance observer-based input-output finite-time control of a class of nonlinear systems with one-sided Lipschitz condition, as well as multiple disturbances. Firstly, a disturbance observer is constructed to estimate the disturbance generated by an exogenous system. Secondly, by integrating the estimation of disturbance with a classical state feedback control law, a composite control law is designed and sufficient conditions for input-output finite-time stability (IO-FTS) of the closed-loop system are attained. Such conditions can be converted into linear matrix inequalities (LMIs). Finally, two examples are given to show the effectiveness of the proposed method.

Highlights

The robust Lyapunov stability reflects the asymptotic behavior; that is, the result only is achieved in an infinite-time interval
A reduced-order disturbance observer is designed to estimate the disturbance generated by this exogenous system
This paper investigates the problem of disturbance observerbased input-output finite-time control of a class of nonlinear systems with one-sided Lipschitz condition, as well as multiple disturbances

Summary

Introduction

The robust Lyapunov stability reflects the asymptotic behavior; that is, the result only is achieved in an infinite-time interval. The definition of input-output finite-time stability (IO-FTS) has been firstly introduced in [5], which is a more practical concept and means that, given a class of norm-bounded input signals over a specified time interval of length T, the outputs of the system do not exceed an assigned threshold during such time interval. Mathematical Problems in Engineering there are few results about disturbance observer-based inputoutput finite-time control of nonlinear systems with onesided Lipschitz condition, which motivates our study. This paper considers disturbance observer-based inputoutput finite-time control of a class of nonlinear systems with one-sided Lipschitz condition, as well as disturbances.

Problem Formulation

IO-FTS Analysis

The Examples

Conclusion