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

Authors: Haddad W. M.; Chellaboina V.; Kablar N. A.

Source: International Journal of Control, Volume 74, Number 17, 20 November 2001 , pp. 1659-1677(19)

Publisher: Taylor and Francis Ltd

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Abstract:

In a companion paper (Nonlinear Impulsive Dynamical Systems. Part I: Stability and Dissipativity) Lyapunov and invariant set stability theorems and dissipativity theory were developed for non-linear impulsive dynamical systems. In this paper we build on these results to develop general stability criteria for feedback interconnections of non-linear impulsive systems. In addition, 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 specific way to an underlying Lyapunov function that guarantees asymptotic stability of the non-linear closed-loop impulsive system. Furthermore, the Lyapunov function is shown to be a solution of a steady-state, hybrid Hamilton–Jacobi–Bellman equation.

Language: English

Document Type: Research article

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