ROBUST REGULATION OF A CLASS OF NONLINEAR SINGULARLY PERTURBED SYSTEMS R. Amjadifard* M. J. Yazdanpanah** M. T. H. Beheshti* *Department of Electrical Engineering, Faculty of Engineering, Tarbiat Modarres University, Tehran, Iran ** Control & Intelligent Processing Center of Excellence, Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran Abstract: In this paper, robust regulation of a class of nonlinear singularly perturbed systems, via nonlinear ∞ H approach is considered. Under appropriate assumptions, it is shown through two new theorems that the existence of a positive definite solution for the Hamilton-Jacobi-Isaacs inequality related to the problem of disturbance attenuation for the main singularly perturbed system, can be related to the existence of a solution of a (simpler) Hamilton-Jacobi-Isaacs inequality arising in the problem of disturbance attenuation for the reduced-order system. Copyright © 2005 IFAC Keyword: Nonlinear systems, Singular perturbation, Robust performance, H-infinity control. 1. INTRODUCTION One drawback of ∞ H design is that the order of the controller is at least equal to the order of the plant, and larger if, as is common, weights are included in the design (Amjadifard, et al., 2005). An approach to reduced-order controller design for a class of nonlinear composite systems is introduced by Isidori and Tarn (1995) and Isidori (1999). In these references, the problem of robust disturbance attenuation with internal stability via ∞ H controller for a class of nonlinear composite systems has been investigated. In particular, it has been shown by Isidori and Tarn (1995) that the existence of a positive definite solution for the Hamilton-Jacobi- Isaacs (HJI) inequality arising in the problem of disturbance attenuation for a nonlinear composite system, can be related to the existence of a solution of a (simpler) HJI inequality arising in the problem of disturbance attenuation for a plant which is a part of the main plant. The problem of disturbance attenuation with local internal stability, via state feedback is to find, if possible, a feedback law such that the corresponding closed loop system has a locally asymptotically stable equilibrium and a 2 L gain from the input disturbance to the regulated output, less than or equal to a prescribed value γ (Isidori and Tarn, 1995). For more details about 2 L gain refer to (Ball, et al., 1993; Van der Schaft, 1992; Van der Schaft, 1991; and Isidori, 1991). Problem of disturbance attenuation via ∞ H approach for linear and nonlinear singularly perturbed systems has been considered in many references. In (Fridman, 2001), the mentioned problem has been solved by considering the related HJI inequality, defining reduced Hamiltonian system, fast ε -independent PDE, and then constructing the ∞ H composite controller. On the other hand, Yazdanpanah, et al. (1997) introduced a new algorithm for the problem of robust regulation for linear singularly perturbed