  This paper presents an iterative algorithm to compute a Robust Control
Invariant (RCI) set, along with an invariance-inducing control law, for Linear
Parameter-Varying (LPV) systems. As the real-time measurements of the
scheduling parameters are typically available, in the presented formulation, we
allow the RCI set description along with the invariance-inducing controller to
be scheduling parameter dependent. The considered formulation thus leads to
parameter-dependent conditions for the set invariance, which are replaced by
sufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation.
These LMI conditions are then combined with a novel volume maximization
approach in a Semidefinite Programming (SDP) problem, which aims at computing
the desirably large RCI set. In addition to ensuring invariance, it is also
possible to guarantee performance within the RCI set by imposing a chosen
quadratic performance level as an additional constraint in the SDP problem. The
reported numerical example shows that the presented iterative algorithm can
generate invariant sets which are larger than the maximal RCI sets computed
without exploiting scheduling parameter information.
