State decomposition and the enlargement of stabilizable regions

Ellipsoidal sets form a popular choice for terminal invariant feasible sets in MPC. Requiring however terminal states to lie within such ellipsoidal sets leads to a quadratic condition which increases online computation. Low complexity polytopes offer a convenient remedy and allow for robust MPC that require the online solution of a Linear Program. The benefit is both in terms of reduced computation and size of stabilizable sets. Here we show how state decomposition can be deployed in order to combine several low complexity polytopes and enlarge the terminal set (and stabilizable set) through the use of the convex hull of a set of invariant feasible sets. Moreover decomposition allows for the introduction of further degrees of freedom (d.o.f.) which can be exploited in the improvement of dynamic performance.