Computing State Invariants Using Point-Wise Integral Quadratic Constraints and the S-procedure

This paper deals with the problem of computing ellipsoidal state invariant sets for uncertain systems that consist of a nominal part and an uncertainty feedback operator. The set of allowable uncertainty operators is characterized using point-wise integral quadratic constraints (IQCs). The proposed solution methodology combines the S-procedure and the notion of point-wise IQCs in a novel way. The approach allows for a point-wise characterization of the disturbance inputs and involves solving a grid of convex optimization problems. The paper concludes with an illustrative example.