Robust H∞ stabilization of a nonlinear uncertain system via a stable nonlinear output feedback controller

Authors:
Hendra G. Harno;Ian R. Petersen
Affiliations:
School of Information Technology and Electrical Engineering, University of New South Wales, Australian Defence Force Academy, Canberra, ACT, Australia;School of Information Technology and Electrical Engineering, University of New South Wales, Australian Defence Force Academy, Canberra, ACT, Australia
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

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Abstract

A new approach to solving a nonlinear robust H∞ control problem using a stable nonlinear output feedback controller is presented in this paper. The particular class of nonlinear uncertain systems being considered is characterized in terms of Integral Quadratic Constraints and Global Lipschitz Conditions describing the admissible uncertainty and nonlinearity, respectively. The nonlinear controller is then constructed by including a copy of the system nonlinearity in the structure of the linear controller. The aim is to enable the controller to exploit the nonlinearity of the system such that it will absolutely stabilize the closed loop nonlinear system and achieve a specified disturbance attenuation level. This method involves the stabilizing solutions of a pair of algebraic Riccati equations.