Stability criteria for first-order dynamical systems in a behavioral framework

This paper addresses the stability of dynamical systems described by first-order differential equations in the behavioral framework. Some algebraic stability criteria are derived under the assumption that the behavior does not include distributions. The derivation of our criteria is based on quadratic differential forms and two-variable polynomial matrices (cf. Willems and Trentelman, SIAM J. Optim. Control 36 (1998) 1703-1749; Willems, Proceedings of the 30th IEEE Conference on Decision and Control, 1991, pp. 900-904), which are appropriate tools for system synthesis and analysis in the behavioral approach. Thus, our result and approach will contribute to the developement of the behavioral system theory. Furthermore, our criteria are represented in terms of linear matrix inequalities and algebraic matrix equations, which leads to easy examination of the stability with the help of appropriate software packages. (C) 2000 Elsevier Science B.V. All rights reserved.