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

Peiling Fu (1) , Jie Chen (1) , Silviu-Iulian Niculescu (2)

1 Department of Electrical Engineering [Riverside]
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

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. © 2006 Elsevier Ltd. All rights reserved.

Mots clés: 2-D system; Generalized eigenvalue; Matrix pencil; Stability

Domaines: Automatique / Robotique

Peiling Fu, Jie Chen, Silviu-Iulian Niculescu. Generalized eigenvalue-based stability tests for 2-D linear systems Necessary and sufficient conditions. Automatica, 2006, 42 (9), pp.1569-1576. ⟨10.1016/j.automatica.2006.04.015⟩. ⟨hal-02294068⟩