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Stability analysis of positive descriptor systems

Please always quote using this URN:urn:nbn:de:0296-matheon-3895
  • In this paper, we discuss stability properties of positive descriptor systems in the continuous-time as well as in the discrete-time case. We present different characterisations of positivity and establish generalised stability criteria for the case of positive descriptor systems. We show that if the spectral projector onto the right finite deflating subspace of the matrix pair $(E,A)$ is non-negative, then all stability criteria for standard positive systems take a comparably simple form in the positive descriptor case. Furthermore, we provide sufficient conditions that guarantee entry-wise non-negativity along with positive semi-definiteness of solutions of generalised projected Lyapunov equations. As an application of the framework established throughout this paper, we exemplarily generalise two criteria for the stability of two switched standard positive systems under arbitrary switching to the descriptor case.

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Metadaten
Author:Elena Virnik
URN:urn:nbn:de:0296-matheon-3895
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/04/05
Release Date:2007/03/05
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A22 Matrix pencils [See also 47A56]
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A24 Matrix equations and identities
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp; lp, etc.)
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D20 Asymptotic stability
Preprint Number:384
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