A LINEAR MATRIX INEQUALITY APPROACH TO PEAK-TO-PEAK GAIN MINIMIZATION

In this paper we take a new approach to the problem of peak-to-peak ga in minimization (the L(1) or induced L(infinity) problem). This is don e in an effort to circumvent the complexity problems of other approach es. Instead of minimizing the induced L(infinity) norm, we minimize th e -norm, the best upper bound on the induced L(infinity) norm obtaina ble by bounding the reachable set with inescapable ellipsoids. Control ler and filter synthesis for -norm minimization reduces to minimizing a continuous function of a single real variable. This function can be evaluated, in the most complicated case, by solving a Riccati equatio n followed by an LMI eigenvalue problem. We contend that synthesis is practical now, but a key computational question-is the function to be minimized convex?-remains open. The filters and controllers that resul t from this approach are at most the same order as the plant, as in th e case of LQG and H-infinity design.