Peak-to-Peak Gain Minimization for Uncertain Linear Discrete Systems: A Matrix Inequality Approach

A matrix inequality approach to peak-to-peak gain minimization for a class of uncertain linear discrete systems is studied. We minimize the *-norm, which is the best upper bound on the induced L∞ norm obtained by bounding the reachable set with inescapable ellipsoids, instead of minimizing the induced L∞ norm directly. Based on this idea, the problems of robust peak-to-peak gain minimization and controller synthesis are reduced to solving the feasibility problems of a set of matrix inequalities. A numerical example is used to demonstrate the feasibility and effectiveness of the presented method.