A nonlinear application of a Lyapunov technique for assuring global performance bounds

Abstract

In this paper we consider the stability and performance problem of nonlinear systems using a Lyapunov technique. The upper or lower bounds can be provided assuming that a Lyapunov function satisfies a Hamiltonian inequality for all admissible states. Also, suboptimal control laws with guaranteed performance bounds can be derived with this technique. The technique has been applied on rate and attitude control for sounding rockets. As an example, a rate control algorithm is elaborated showing the main ideas presented in this paper: (1) the Lyapunov function provides a global performance bound; (2) a control law is derived based on the Lyapunov function; and (3) the candidate Lyapunov function is parametrized and improved bounds are obtained using parameter optimization.