On interconnections of discontinuous dynamical systems An input-to-state stability approach
conference paper
In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems (DDS) adopting non-smooth ISS Lyapunov functions. The main motivation for investigating non-smooth ISS Lyapunov functions is the success of “multiple Lyapunov functions” in the stability analysis of hybrid systems. This paper proposes an extension of the well-known Filippov solution concept, that is appropriate for ‘open’ systems so as to allow interconnections of DDS. It is proven that the existence of a non-smooth ISS Lyapunov function for a DDS implies ISS. In addition, a (small gain) ISS interconnection theorem is derived for two DDS that both admit a non-smooth ISS Lyapunov function. This result is constructive in the sense that an explicit ISS Lyapunov function for the interconnected system is given. It is shown how these results can be applied to construct piecewise quadratic ISS Lyapunov functions for piecewise linear systems (including sliding motions) via linear matrix inequalities.
Topics
TNO Identifier
953878
ISSN
01912216
ISBN
1424414989
Publisher
IEEE
Article nr.
4434742
Source title
Proceedings of the IEEE Conference on Decision and Control, 46th IEEE Conference on Decision and Control 2007, CDC, 12 December 2007 through 14 December 2007
Pages
109-114
Files
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