Convex relaxation techniques for set-membership identification of LPV systems

Set-membership identification of single-input single-output linear parameter varying models is considered in the paper under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise. First, we show that the problem of computing the parameter uncertainty intervals requires the solutions to a number of nonconvex optimization problems. Then, on the basis of the analysis of the regressor structure, we present some ad hoc convex relaxation schemes to compute parameter bounds by means of semidefinite optimization. Advantages of the new techniques with respect to previously published results are discussed both theoretically and by means of simulations.