Computation of low-complexity control-invariant sets for systems with uncertain parameter dependence

Journal article, 2019

This paper considers the problem of computing a low-complexity robust control-invariant (LC-RCI) set for uncertain systems, along with a static linear state-feedback law. The LC-RCI set, assumed to be symmetric around the origin and described by the same number of affine inequalities as twice the dimension of the state vector, is the result of an iterative procedure, where semi-definite programs (SDPs) are solved at each step. The SDPs are formulated to increase the LC-RCI volume at each step, subject to tractable reformulations of the system constraints as well as the invariance condition (in the form of standard or dilated LMIs), and a new approach to determinant maximization. The two proposed algorithms are applicable to systems with rational parameter dependence, which cannot be handled with the existing similar approaches without introducing additional conservatism.