Singular Perturbation Method for Robust Control of Nonlinear Systems - Mogaver, Hadi Bafandegan; Zare, Asef; Tanhatalab, Mohammad Rasoul (Iraqi Journal for Electrical and Electronic Engineering, 2010)
In this paper, we consider robust control of nonlinear systems, via inclusion nonlinear systems solution and $H_{∞}$ controller using singular perturbation method. First, using a technique for solving inclusion nonlinear systems, we transform the nonlinear system to an ordinary nonlinear system. Then using normal form equations, we eliminate the nonlinear part of the system matrix of equations of the system and transform it to a linear diagonal form. Separating new equations into slow and fast subsystems, due to the singular perturbation method and with the assumption of norm-boundedness of the fast dynamics, we can treat them as disturbance and design an $H_{∞}$ controller for a system with a lower order than the original one that stabilizes the overall closed loop system. The proposed method is applied to a nominal system.