In this paper the extension of LaSalle’s Invariance Principle for switched nonlinear systems is studied. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, in this paper we allow the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle’s Invariance Principle for global ...

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2 + ε moment for the step of the walk uniformly in the environment. The main point behind ...