Abstract
This paper considers the problem of robust \(H_{\infty}\) control for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. By using the linear matrix inequality (LMI) approach, a sufficient condition is presented for a prescribed uncertain singular system with time-delay to have generalized quadratic stability and \(H_{\infty}\) performance. Furthermore, the design methods of state feedback controllers are considered such that the resulting closed-loop system has generalized quadratic stability with \(H_{\infty}\) performance. By means of matrix inequalities, sufficient conditions are derived for the existence of memory-less and memorial static state feedback controllers. The controllers are obtained by the solutions of matrix inequalities.
Highlights
It is well known that a real system inevitably contains some uncertain parameters because of work environment change, measure error, model approximation and so on
Robust H∞ control theory has been perfectly developed over the last decade, most of the results were developed based on uncertain linear systems [ – ]
For the singular system, robust H∞ control problem has been little considered with uncertainties and time-delay recently
Summary
It is well known that a real system inevitably contains some uncertain parameters because of work environment change, measure error, model approximation and so on. For the singular system, robust H∞ control problem has been little considered with uncertainties and time-delay recently. Definition [ ] The uncertain singular delay system ( ) is said to be robust stable if system ( ) with u(t) ≡ and ω(t) ≡ is regular, impulse free and asymptotically stable for all admissible uncertainties A, Ad. Definition [ ] The uncertain singular delay system ( ) is said to be generalized quadratically stable if there exists a matrix X > such that The robust H∞ problem we consider in this paper is, for an uncertain singular delay system and a given constant γ > , under zero initial state if z(t) ≤ γ ω(t) , ∀ω(t) ∈ L [ , ∞) for all admissible uncertainties, we say the system has H∞ performance γ
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