Invariant convex approximations of the minimal robust invariant set for linear difference inclusions

Abstract

In this article, we propose a new computationally efficient algorithm for computing an outer convex robust positively invariant (RPI) approximation to the minimal robust positively invariant (mRPI) set for polytypic linear difference inclusion (PLDI) systems with additive disturbances. The LDI modelling framework is useful to analyse parametrically uncertain, time-varying linear system or switching linear discrete-time systems. The disturbance which is considered in this paper, is bounded by a polytypic set and acts additively on the state of the system. It is also assumed that the nominal LDI system is absolutely asymptotically stable by a stabilizing linear state feedback. The accuracy of the approximation can be set in advance. The proposed algorithm has far less computational burden in comparison with existing algorithms.