Robust pole-clustering for descriptor systems a strict LMI characterization

Abstract

This paper tackles the problem of the characterization of robust pole-clustering for descriptor systems using linear matrix inequalities (LMI). It states a necessary and sufficient condition for a descriptor system to be impulse free and to have its finite poles in a specified convex region of the complex plane. A sufficient condition to guarantee this result in the presence of norm-bounded uncertainties is established. The results are expressed in terms of strict LMIs, thus they are numerically tractable with LMI optimization tools. Numerical examples are given.

Qualitative analysis of switched discrete-time descriptor systems

“…A practical method of finding such a combination is to use the matrix inequality based condition proposed in [6].…”

“…Therefore, descriptor systems are recognized as much superior to state space systems. There have been reported many works on descriptor systems, which studied feedback stabilization [1,2], Lyapunov stability theory [2,3], the matrix inequality approach [4] for stabilization, robust pole-clustering, 2 H and/or ∞ H control [5][6][7][8]. In the last two decades, there has been increasing interest in stability analysis and design for switched systems [9][10][11][12][13].…”

Controller and observer designs for a class of TS descriptor systems with pole placement constraint

“…Lemma 1: [6] The input free LTI descriptor system E ẋ(t) = Ax(t), where E and A ∈ R n×n , is D-admissible if and only if there exists a symmetric positive definite matrix P ∈ R n×n and a matrix S ∈ R (n−r)×(n−r) verifying…”