Further Remarks on Invariance Properties of Time-Delay Systems Available to Purchase

For various problems of practical importance, such as disturbance rejection or constrained control, the determination of invariant sets provides insightful information on the influence of unknown bounded signals on the dynamical system behavior. In order to characterize the effect of those signals on the system, the determination of the minimal robust positively invariant (mRPI) set is of great interest. On the other side, the presence of time delays is ubiquitous in process control and it seems natural to use invariant set theory to analyze time delay systems affected by additive disturbance. The present paper deals with computation and characterization of the delay-independent minimal robust positively invariant region in the set-theoretic framework. The Banach fixed point theorem will be used to specify the existence and uniqueness conditions for this set. Here we also provide a procedure for the construction of invariant approximations of this limit set as well as discussion on the efficient computation for practical usage. Supplementary, at the end is pointed out an interesting correlation between proposed results and existence of the mRPI sets for switching dynamics. In this study we are particularly interested in discrete time systems. Outlined results are confirmed by a numerical example.