Abstract
Abstract—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
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 46th Conference on Decision and Control (CDC 2007) 12-14 December 2007, New Orleans, Louisiana |
| Place of Publication | Piscataway |
| Publisher | Institute of Electrical and Electronics Engineers |
| Pages | 109-114 |
| ISBN (Print) | 978-1-4244-1498-7 |
| DOIs | |
| Publication status | Published - 2007 |