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

Authors:
Magdi Sadek Mahmoud;Mohamed Tawfik Sadek
Affiliations:
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
Venue:
International Journal of Systems, Control and Communications
Year:
2011

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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.