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

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.