Quasi-integral-input-to-state stability for switched nonlinear systems

In this paper we introduce and give sufficient conditions for the quasi-iISS property for switched nonlinear systems under dwell-time switching signals. Unlike previous works, our dwell-time bound does not rely on the knowledge of the state but it relies only on the system initial condition and the bound on the input energy. We prove, through a counterexample, that knowledge of the system initial state and bound on input energy is necessary for the estimation of a dwell-time that guarantees quasi-iISS for the switched system. An illustrative example is also included.