This paper considers Lyapunov stability of discontinuous dynamical systems. It is assumed that discontinuities in the system dynamics are caused by some internal (e.g. component failures), and/or external (e.g. controller commands) discrete events. This kind of systems are often called Hybrid Dynamical Systems. Three cases are discussed in this work. First, we consider that a set of continuous-state systems is given and each system from the set shares a common Lyapunov function. Second, stability of sequentially switched systems is investigated by means of multiple Lyapunov functions. Third, some preliminary results are provided for the case when a hybrid system switches between systems with parametric uncertainty.
Proceedings of the 4th IEEE Mediterranean Symposium of New Directions in Control and Automation
Abdallah, Chaouki T.; R. Fierro; and F.L. Lewis. "Common, multiple and parametric Lyapunov functions for a class of hybrid dynamical systems." Proceedings of the 4th IEEE Mediterranean Symposium of New Directions in Control and Automation (1996): 77-82. https://digitalrepository.unm.edu/ece_fsp/39