Lyapunov stability of 2D finite-dimensional behaviours

• Published in: International journal of control Vol. 84; no. 4; pp. 737 - 745
• Main Authors: Avelli, D. Napp, Rapisarda, P., Rocha, P.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.04.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: 2-D system; Applied sciences; Behavior; behavioural approach; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; Lyapunov function; quadratic difference form; Studies; Cone; Stabilization; behavioural approach; Difference equation; Optimization; Behavioral analysis; 2-D system; Distributed control; Signal processing; quadratic difference form; Quadratic form; Multidimensional system; Lyapunov function; Quadratic function
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2011.575800

In this article we investigate a Lyapunov approach to the stability of finite-dimensional 2D systems. We use the behavioural framework and consider a notion of stability following the ideas in Pillai and Shankar [H. Pillai and S. Shankar ( 1998 ). A Behavioral Approach to Control of Distributed Systems, SIAM Journal of Control and Optimization, 37, 388-408], Rocha [P. Rocha ( 2008 ). Stabilization of Multidimensional Behaviors, Multidimensional Systems and Signal Processing, 19, 273-286], Valcher [M. Valcher ( 2000 ). Characteristic Cones and Stability Properties of Two-dimensional Autonomous Behaviors, IEEE Transactions on Circuits and Systems, Part I, CAS-47, 290-302]. We characterise stability in terms of the existence of a (quadratic) Lyapunov function and provide a constructive algorithm for the computation of all such Lyapunov functions.