Non-linear impulsive dynamical systems. Part II: Stability of feedback interconnections and optimality

In a companion paper (Nonlinear Impulsive Dynamical Systems. Part I: Stabil ity and Dissipativity) Lyapunov and invariant set stability theorems and di ssipativity theory were developed for non-linear impulsive dynamical system s. In this paper we build on these results to develop general stability cri teria for feedback interconnections of non-linear impulsive systems. In add ition, a unified framework for hybrid feedback optimal and inverse optimal control involving a hybrid non-linear-non-quadratic performance functional is developed. It is shown that the hybrid cost functional can be evaluated in closed-form as long as the cost functional considered is related in a sp ecific way to an underlying Lyapunov function that guarantees asymptotic st ability of the non-linear closed-loop impulsive system. Furthermore, the Ly apunov function is shown to be a solution of a steady-state, hybrid Hamilto n-Jacobi-Bellman equation.