Stability tests for 2-D systems Exact solutions via matrix pencil conditions

P. 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 exactly by inspecting the generalized eigenvalues of the matrix pencil. The results consequently furnish 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. © IFAC 2005.

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

Domaines: Automatique / Robotique

P. Fu, Jie Chen, Silviu-Iulian Niculescu. Stability tests for 2-D systems Exact solutions via matrix pencil conditions. 5th IFAC Symposium on Robust Control Design, ROCOND'06, Jul 2006, Toulouse, France. pp.423-428. ⟨hal-02294063⟩