Linear filter design for continuous-time polynomial systems with ℒ2-gain guaranteed bound

This paper proposes a technique for the design of full and reduced-order linear filters for continuous-time polynomial systems satisfying a prescribed induced ℒ2-gain. The filter variables appear affinely in a polynomial inequality and are computed by solving a semidefinite program (SDP). Bounds on the filter performance, established in terms of the induced ℒ2 norms between the input noise and the filtering error are then assessed via polynomial storage functions. Results from numerical experiments are presented.