Passivity-Based Stability Analysis and Robust Practical Stabilization of Nonlinear Affine Systems with Non-vanishing Perturbations

Abstract

This paper presents some analyses about the robust practical stability of a class of nonlinear affine systems in the presence of non-vanishing perturbations based on the passivity concept. The given analyses confirm the robust passivity property of the perturbed nonlinear systems in a certain region. Moreover, robust control laws are designed to guarantee the practical stability of the perturbed systems. For this purpose, the control laws are designed in two cases. In the first case, it is assumed that the designer has freedom in choosing the outputs. In the second case, it is assumed that the outputs are predefined. In this case, first it is considered that the nominal system is passive between its inputs and outputs and then the control law is designed as static output feedback law for the perturbed system. Moreover, in the case that the nominal system is not passive, first, a law is designed such that the new nominal system is passive between the virtual inputs and the outputs. Then, the virtual input is designed as a static output feedback law such that the proposed controllers guarantee the practical stability of the perturbed system. Finally, the computer simulations are performed to show the efficacy and applicability of the designed controllers.