Energy-Peak Evaluation of Nonlinear Control Systems under Neglected Dynamics

Abstract The main objective in this paper is to investigate the robust performance degradation for a class of nonlinear systems due to some dynamics that are not taken into account during the controller design stage. This is usually the case in practical applications where a simplified (nonlinear) model is used to design the controller. Therefore, it is expected some performance degradation in the application of such a controller due to the presence of the neglected dynamics. With this purpose, some convex conditions for stability analysis and energy-peak evaluation of nonlinear control systems are given. It is supposed that the nonlinear functions present in the model are subject to bounded uncertainties and that both the simplified model and the neglected dynamics model are affected by polytopic uncertainties. The theoretical conditions providing stability and energy-peak bound on the regulated output of the system despite the presence of uncertainties associated with the nonlinear functions are obtained by means of a parameter dependent Lyapunov function. The proposal is illustrated by numerical examples.