Stability Robustness Conditions for Control Systems with Bounded and Unbounded Nonlinear Gain Elements

Abstract

Taking the stability robustness into account in every aspect is a current trend in control theory. However, major recent efforts have been focused on the stability robustness of linear control systems, and so, results for nonlinear systems seem to be few. In this respect, we will make several attempts to cope with stability problems for control systems having bounded or unbounded nonlinear gain elements. We consider two tpyes of Lyapunov functions : L₂ type functions, i.e., quadratic functions and L₁ Type ones. The former is used to show the stability of systems with bounded gain elements and the latter for systems with unbounded gain characteristics. The existence of such functions assures robust stability for these nonlinear systems against perturbations in the nonlinear gain elements.