Strict positive realness of descriptor systems in state space

Abstract

In this article, we give necessary and sufficient spectral conditions for various notions of strict positive realness for single-input single-output descriptor systems. These conditions only require calculation of eigenvalues of a single matrix. A characterisation of a Kalman–Yacubovich–Popov-like lemma for descriptor systems is also derived, and its implications for the stability of a class of switched descriptor systems are briefly discussed.

Keywords:

• descriptor systems
• Kalman–Yacubovich–Popov lemma
• strict positive realness
• extended strict positive realness

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Corrigendum

Acknowledgement

This work was supported by the Science Foundation Ireland, PI Award 07/IN.1/1901.