On the design of a reduced-order H∞ controller for nonlinear sampled-data systems

Authors:
Yen-Fang Li;Chee-Fai Yung;Hsin Jung
Affiliations:
Department of Electrical Engineering, Ming Hsing University of Science and Technology, Hsin-Chu, Taiwan;Department of Electrical Engineering, National Taiwan Ocean University, Keelung, Taiwan;Department of Electrical Engineering, National Taiwan Ocean University, Keelung, Taiwan
Venue:
International Journal of Systems Science
Year:
2005

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Abstract

In this paper, the problem of designing reduced-order H∞ controllers is studied for nonlinear continuous-time systems with sampled measurements. Using the concepts of dissipativity and differential game, sufficient conditions are derived for the existence of such reduced-order H∞ controllers. These conditions are expressed in terms of the solutions of two Hamilton-Jacobi inequalities, comprising a standard Hamilton-Jacobi inequality and a differential Hamilton-Jacobi inequality with jumps. These Hamilton-Jacobi inequalities are exactly those used in the construction of full-order H∞ controllers. When these conditions hold, state-space formulae are also given for such reduced-order controllers. An illustrative example is also included.