Computation of invariant sets for discrete-time uncertain systems

Abstract

This article proposes novel methods for the computation of state and output bounding sets for discrete-time uncertain systems. The systems under consideration are formed from the interconnection of a nominal linear time-invariant system and an uncertainty operator that is known to lie within a prespecified set. The set of allowable uncertainties is described by a pointwise integral quadratic constraint (IQC), that is, a quadratic constraint that holds for all time-steps. Examples of pointwise IQCs characterizing common uncertainty sets are provided. The exogenous input to the system is assumed to lie in a given polytope or ellipsoid for all time-steps. The proposed methods are illustrated via an example. © 2023 John Wiley & Sons Ltd.