Extending LaSalle's invariance principle to impulsive switched systems with an application to hybrid epidemic dynamics

By introducing the notions of persistent limit set and persistent mode, we extend the classical LaSalle's invariance principle to hybrid systems exhibiting both impulses and switchings. A weak invariance principle is established for such systems, under a weak dwell-time condition on the impulsive and switching signals. This weak invariance principle is then applied to derive two asymptotic stability criteria for impulsive switched systems. As an application of the stability criteria,we investigate a switched SEIR epidemic model with pulse treatment and establish sufficient conditions for the global asymptotic stability of the disease-free solution under weak dwell-time signals.