PD feedback H ∞ $H_{\infty}$ control for uncertain singular neutral systems

Jichun Wang,Qingling Zhang,Dong Xiao

doi:10.1186/s13662-016-0749-y

Abstract

This paper focuses on the problem of proportional-plus-derivative (PD) feedback $H_{\infty}$ control for uncertain singular neutral systems. The parameter uncertainties are assumed to be time-varying norm-bounded and appearing not only in the state matrix but also in the derivative matrix. This paper introduces new effective criteria which make the systems stable and meet the $H_{\infty}$ performance by PD feedback controller. Different from most existing methods, this study attempts to introduce the information between derivative matrices. Based on such an idea, the PD feedback controller for singular neutral systems is first of all proposed which makes the derivative matrices (especially neutral matrix) meet the requirement which guarantees the existence of the solution for the system. So the criteria in this paper are less conservative to some extent. Finally, illustrate examples are given to demonstrate the effectiveness of the proposed approach.

Highlights

1 Introduction Since the late s, interests have been focused on the study of the H∞ control problem [ ] due to its practical and theoretical importance
Various approaches have been developed and a great number of results for continuous systems as well as discrete systems have been reported in the literature: [ ] discussed the State space solutions to standard H and H∞ control problems; [ ] studied delay-dependent robust H∞ controller synthesis for discrete singular delay systems; [ ] stated H∞ control for descriptor systems: a matrix inequalities approach; [ ] addressed non-fragile H∞ control for linear systems with multiplicative controller gain variations
The main objective of this paper is to present the PD feedback controller for neutral singular systems

Summary

Introduction

Since the late s, interests have been focused on the study of the H∞ control problem [ ] due to its practical and theoretical importance. Section presents an H∞ performance analysis of the neutral singular systems and Section designs PD state feedback stabilizing controllers. It is noted that the regularity of the neutral singular system ( a) and the stability of operator can ensure the existence and uniqueness of the solution, which is shown in the following lemma. Theorem For given scalar τ , h > , the nominal system ( a) and ( b) with u(t) = is asymptotically stable with an H∞ disturbance attenuation γ > for all nonzero w(t) ∈ LP [ , +∞] if there exist positive matrices P = PT > , Qi = QTi > (i = , ), U = UT > , and any matrices Nj (j = , ), such that the following LMIs are feasible:.

Stabilizing controllers of uncertain neutral singular system

B X –P

Conclusions