On the Complexity of Computing the Maximal Positive Invariant Set

Computing the maximal (robust) positive invari-ant (M(R)PI) set for linear dynamics and a polyhedral constraint set is well-known in the literature but, the effects and limitations of the different methods employed are not sufficiently clear, especially for high dimensional systems. In this paper we propose a systematic analysis of the existing techniques as well as the application of new ideas to accelerate the computation of the MPI set. This includes new stop conditions for the set recurrence that spans it. We analyze and compare these variations over a dynamical system whose dimension can be arbitrarily increased to draw conclusions about their relative strengths and weaknesses.