Nonlinear impulsive dynamical systems. II. Feedback interconnections and optimality

For part I, see ibid. In part I, Lyapunov and invariant set theorems, and dissipativity theory were developed for nonlinear impulsive dynamical systems. In this part we build on these results to develop general stability criteria for feedback interconnections of nonlinear impulsive systems. In addition, a unified framework for hybrid feedback optimal control involving a hybrid nonlinear-nonquadratic 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 specific way to an underlying Lyapunov function that guarantees asymptotic stability of the nonlinear closed-loop impulsive system. Furthermore, the Lyapunov function is shown to be a solution of a steady-state, hybrid Hamilton-Jacobi-Bellman equation.