Title: Peak-to-peak gain minimisation of uncertain discrete-time systems with variable delays

Authors: Magdi Sadek Mahmoud; Mohamed Tawfik Sadek

Addresses: Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran 31261, Saudi Arabia. ' Electrical Engineering Department, Kuwait University, P.O. Box 5969, Safat, Kuwait

Abstract: In this paper, we provide a novel solution to the problem of peak-to-peak gain minimisation for a class of linear discrete-time systems with time-varying delays. The solution is developed based on minimising the *-norm, which is the best upper bound on the induced L?-norm generated by bounding the reachable set with inescapable ellipsoids, rather than minimising the induced L?-norm directly. We develop sufficient conditions to the solution of the problems of robust L?-gain analysis and robust state-feedback controller synthesis in terms of strict linear matrix inequalities. The developed results are tested on a representative example.

Keywords: time delay systems; peak-to-peak gain minimisation; L1 performance; state feedback; strict LMIs; uncertainty; discrete time systems; linear matrix inequalities.

DOI: 10.1504/IJSCC.2011.043766

International Journal of Systems, Control and Communications, 2011 Vol.3 No.4, pp.456 - 471

Published online: 31 Mar 2015 *

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