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This paper presents an iterative algorithm to compute a Robust ControlInvariant (RCI) set, along with an invariance-inducing control law, for LinearParameter-Varying (LPV) systems. As the real-time measurements of thescheduling parameters are typically available, in the presented formulation, weallow the RCI set description along with the invariance-inducing controller tobe scheduling parameter dependent. The considered formulation thus leads toparameter-dependent conditions for the set invariance, which are replaced bysufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation.These LMI conditions are then combined with a novel volume maximizationapproach in a Semidefinite Programming (SDP) problem, which aims at computingthe desirably large RCI set. In addition to ensuring invariance, it is alsopossible to guarantee performance within the RCI set by imposing a chosenquadratic performance level as an additional constraint in the SDP problem. Thereported numerical example shows that the presented iterative algorithm cangenerate invariant sets which are larger than the maximal RCI sets computedwithout exploiting scheduling parameter information.

Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance