On characterizations of the input-to-state stability property
Systems & Control Letters
A Smooth Converse Lyapunov Theorem for Robust Stability
SIAM Journal on Control and Optimization
A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems
Automatica (Journal of IFAC)
Stability analysis of hybrid systems via small-gain theorems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Brief paper: Tracking and synchronisation for a class of PWA systems
Automatica (Journal of IFAC)
Input-to-state stability and interconnections of discontinuous dynamical systems
Automatica (Journal of IFAC)
A Decompositional Proof Scheme for Automated Convergence Proofs of Stochastic Hybrid Systems
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
Minimal Control Synthesis Adaptive Control of Continuous Bimodal Piecewise Affine Systems
SIAM Journal on Control and Optimization
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In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems adopting Filippov's solution concept and using non-smooth ISS Lyapunov functions. The main motivation for adopting non-smooth ISS Lyapunov functions is that "multiple Lyapunov functions" are commonly used in the stability theory for hybrid systems. We will show that the existence of a non-smooth (but Lipschitz continuous) ISS Lyapunov function for a discontinuous system implies ISS. Next, we will prove an ISS interconnection theorem for two discontinuous dynamical systems that both admit an ISS Lyapunov function. The interconnection will be shown to be globally asymptotically stable under a small gain condition. The developed ISS theory will be applied to observer-based controller design for a class of piecewise linear systems using an observer structure proposed by the authors. The LMI-based design of the state feedback and the observer can be performed separately.