On bounds of Input-Output systems. Reachability set determination and polyhedral constraints verification

摘要

In this paper some results about constrained Input-Output systems are presented. The considered framework is the Callier-Desoer Class of convolution systems, which covers both finite dimensional systems and infinite dimensional ones such as systems with time delays. Based on bounds calculus for the input-output gain of the convolution kernel, and convex sets properties, a characterization of the output reachable set is first presented. Necessary and sufficient conditions are then derived to warrant the constraints meeting, and some invariance properties, when the system is subject to polyhedral constraints on both its inputs and outputs. A numerical example is given to illustrate the proposed approach on a time delayed system.