A Unified Framework For The H-Infinity Mixed-Sensitivity Design Of Fixed Structure Controllers Through Putinar Positivstellensatz

In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H-infinity mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H-infinity controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach.