Eliminating Impulse for Descriptor System by Derivative Output Feedback

Jian Li,Liang Qiao,Qingling Zhang,Yufa Teng,Jinghao Li

doi:10.1155/2014/265601

Abstract

The problem of impulse elimination for descriptor system by derivative output feedback is investigated in this paper. Based on a novelly restricted system equivalence between matrix pencils, the range of dynamical order of the resultant closed loop descriptor system is given. Then, for the different dynamical order, sufficient conditions for the existence of derivative output feedback to ensure the resultant closed loop system to be impulse free are derived, and the corresponding derivative output feedback controllers are provided. Finally, simulation examples are given to show the consistence with the theoretical results obtained in this paper.

Highlights

Descriptor systems are referred to as singular systems, implicit systems, differential algebraic systems, semistate systems, or generalized state space systems
The control of descriptor systems has been extensively studied in past years and a great number of results based on the theory of standard state space systems have been generalized to descriptor systems [1,2,3,4,5]
Eliminating impulse by proportional and derivative output feedback has been investigated by [13, 20,21,22,23,24], the matrix factorizations used in these papers are complex and creative; this paper aims to address the effect of derivative output feedback on the impulsiveness alone and provide a tractable and alternative method to design the derivative output feedback

Summary

Introduction

Descriptor systems are referred to as singular systems, implicit systems, differential algebraic systems, semistate systems, or generalized state space systems. Descriptor systems’ models are more convenient and natural than standard state space systems’ models in describing practical systems, such as interconnected large-scale systems, economic systems, networks, power systems, and biological systems [1, 2]. Due to this reason, the control of descriptor systems has been extensively studied in past years and a great number of results based on the theory of standard state space systems have been generalized to descriptor systems [1,2,3,4,5]. Let us take an example to illustrate this fact; a three-dimensional descriptor system is given by

Objectives

Results

Conclusion