On the Existence of Control Lyapunov Functions and State-Feedback Laws for Hybrid Systems
- 23 May 2013
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 58 (12), 3242-3248
- https://doi.org/10.1109/tac.2013.2264851
Abstract
For a class of hybrid systems given in terms of constrained differential and difference equations/inclusions, we study the existence of control Lyapunov functions when compact sets are asymptotically stable as well as the stabilizability properties guaranteed when control Lyapunov functions exist. An existence result asserting that asymptotic stabilizability of a compact set implies the existence of a smooth control Lyapunov function is established. When control Lyapunov functions are available, conditions guaranteeing the existence of stabilizing continuous state-feedback control laws are provided.Keywords
This publication has 19 references indexed in Scilit:
- Control Lyapunov functions and stabilizability of compact sets for hybrid systemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2011
- Results on input-to-output and input-output-to-state stability for hybrid systems and their interconnectionsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2010
- Hybrid dynamical systemsIEEE Control Systems, 2009
- Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic StabilityIEEE Transactions on Automatic Control, 2007
- Solutions to hybrid inclusions via set and graphical convergence with stability theory applicationsAutomatica, 2006
- Discrete-time asymptotic controllability implies smooth control-Lyapunov functionSystems & Control Letters, 2004
- Weak Converse Lyapunov Theorems and Control-Lyapunov FunctionsSIAM Journal on Control and Optimization, 2004
- On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradientsESAIM: Control, Optimisation and Calculus of Variations, 2001
- Existence of Lipschitz and Semiconcave Control-Lyapunov FunctionsSIAM Journal on Control and Optimization, 2000
- Variational AnalysisPublished by Springer Science and Business Media LLC ,1998