| Summary: | In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> 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.
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