Robust Stabilization of Non-Minimum Phase Nonlinear Systems with Non-Affine Internal Dynamics: Application on TORA System

This article studies a class of non-minimum phase nonlinear systems with non-affine internal dynamics. The non-minimum phase feature, along with the non-affine internal dynamic, makes complexities in the process of controller design for this class of systems. In this paper, a new approach is presented for designing the control law for these systems. In the proposed method, the system’s equations, considering the system’s relative degree, are rewritten in the normal form. The design procedure of the control law, in the considered system, has three main steps. First, using the constraint optimization approach, the virtual control law is designed to stabilize the non-minimum phase and non-affine internal dynamics. Then, by designed virtual controller and combination with backstepping method, the proper sliding surface is extracted and, finally, based on the proposed sliding surface, a robust control law is designed to stabilize all of the system’s state variables. The simulation results on the TORA system show the efficiency of the proposed approach in the robust stabilization of this class of nonlinear systems.