Abstract
In this paper we will extend the input-to-state stability (ISS) framework to continuous-time <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">discontinuous</i> dynamical systems (DDS) adopting <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-smooth</i> 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
