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Research Papers

# Robust Stabilization for a Class of Nonlinear Singularly Perturbed Systems

[+] Author and Article Information

Department of Computer Engineering, Faculty of Engineering,  Tarbiat Moallem University, Tehran 15719-14911, Iranamjadifard@tmu.ac.ir

M. T. H. Beheshti

Department of Electrical Engineering, Faculty of Engineering,  Tarbiat Modarres University, Tehran 9413676511, Iranmbehesht@modares.ac.ir

M. J. Yazdanpanah

Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering,  University of Tehran, Tehran 14395-515, Iranyazdan@t.ac.ir

J. Dyn. Sys., Meas., Control 133(5), 051004 (Jul 27, 2011) (6 pages) doi:10.1115/1.4003383 History: Received February 10, 2010; Revised December 08, 2010; Published July 27, 2011; Online July 27, 2011

## Abstract

In this paper, the problem of disturbance attenuation with internal stability for a class of nonlinear singularly perturbed systems via nonlinear $H∞$ approach is studied. It is shown through a useful theorem that under appropriate assumptions, the problem of disturbance attenuation for the main system may be related to the problem of disturbance attenuation for the reduced-order system. This is carried out by a new approach in which we use the quasi-steady state of fast variables. Therefore, the problem of existence of a positive definite solution for the Hamilton–Jacobi–Isaacs (HJI) inequality related to the main system leads to the problem of existence of a solution of a simpler HJI inequality related to the reduced-order system.

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## Figures

Figure 1

Open loop response of system 19 with the input disturbance w=sin2t and initial conditions x10=1.35 and x20=0.1

Figure 2

Closed loop response of system 19 with the composite controller, input disturbance w=sin2t, and initial conditions x10=1.35 and x20=0.1

Figure 3

Closed loop response of system 19, with w=1.2sin2t and initial conditions x10=0.9 and x20=0.5

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