On efficient computation of low-complexity controlled invariant sets for uncertain linear systems

Abstract

A method is presented for determining invariant low-complexity polytopic sets and associated linear feedback laws for linear systems with polytopic uncertainty. Conditions based on the relationship between 2- and ∞-norms are used to define an initial invariant low-complexity polytope as the solution of a semi-definite program. The problem of computing a maximal controlled invariant low-complexity polytopic set is then formulated as a bilinearly constrained problem, and a relaxation of this problem is derived as an iterative sequence of convex programs. The proposed method scales linearly with the state dimension, which allows the possibility of determining low-complexity robust controlled invariant sets for high-order systems.