Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps

Xiaoming Su,Adiya Bao

doi:10.1155/2015/950685

Abstract

The finite-timeH∞control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-timeH∞for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfiesL2gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.

Highlights

In practice a system could be stable but completely useless because it possesses undesirable transient performances
finite-time stability (FTS) in the presence of exogenous inputs leads to the concept of finitetime boundedness (FTB)
In other words a system is said to be FTB if, given a bound on the initial condition and a characterization of the set of admissible inputs, the state variables remain below the prescribed limit for all inputs in the set

Summary

Introduction

In practice a system could be stable but completely useless because it possesses undesirable transient performances. Sufficient conditions for FTS and finite-time stabilization have been provided in the control literature; see [8,9,10]. The finite-time stability (FTS) problems of time-varying linear singular system have been studied [15,16,17]. The system we consider in this paper is a class of uncertain linear time-varying descriptor system with finite state jumps and time-varying norm-bounded disturbance. In [24, 25], sufficient conditions for FTS of linear time-varying singular system with impulses at fixed times were given in terms of matrix inequalities.

Problem Statement

Main Result

Numerical Example

Conclusions