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Strict positive realness of descriptor systems in state space. (English) Zbl 1213.93076

Int. J. Control 83, No. 9, 1799-1809 (2010); corrigendum ibid. 85, No. 5, 612 (2012).
Summary: 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-Yakubovich-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.

MSC:

93C05 Linear systems in control theory
93D25 Input-output approaches in control theory
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References:

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