Singular perturbation method for robust control of nonlinear systems

In this paper, we consider robust control of nonlinear systems, via inclusion nonlinear systems solution and H_∞ controller using singular perturbation method. First, using technique for solving inclusion nonlinear systems, we transform the nonlinear system to ordinary nonlinear system. Then using normal form equations, we eliminate the nonlinear part of the system matrix of equations of system and transform it to a linear diagonal form. Separating new equations to 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 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.