Brief paper: Generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions

Authors:
Peilin Fu;Jie Chen;Silviu-Iulian Niculescu
Affiliations:
Department of Electrical Engineering, University of California, Riverside, CA 92521, USA;Department of Electrical Engineering, University of California, Riverside, CA 92521, USA;Centre de Recherche de Royallieu, HeuDiaSyC (UMR CNRS 6599), Université de Technologie de Compiègne, BP 20529, 60205, Compiègne, France
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Correspondence: A counterexample to "Generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions" by Fu, P., Chen, J., and S.I. Niculescu

Automatica (Journal of IFAC)
Correspondence: Author's reply to "A counterexample to Generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions"

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Lyapunov stability analysis of higher-order 2-D systems

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Time-relevant stability of 2D systems

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Abstract

This paper studies the stability of 2-D dynamic systems. We consider systems characterized by 2-D polynomials and 2-D state-space descriptions. For each description, we derive necessary and sufficient stability conditions, which all require only the computation of a constant matrix pencil. The stability of the underlying system can then be determined by inspecting the generalized eigenvalues of the matrix pencil. The results consequently yield 2-D stability tests that can be checked both efficiently and with high precision. Additionally, frequency-sweeping tests are also obtained which complement the matrix-pencil tests and are likely to be more advantageous analytically.