Glizer, Valery Y. (Technion-Israel Institute of Technology)

On First-Order Controllability Conditions for a Class of Singularly Perturbed Systems with Delays

Scheduled for presentation during the Regular Session "Infinite Dimensional and Distributed Parameter Systems III" (ThP06), Thursday, July 27, 2006, 15:45−16:10, Room G

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

A singularly perturbed linear time-dependent controlled system with a small point-wise delay in the state variable is considered. Two much simpler parameter-free systems, the slow and fast ones, are associated with the original system. It was established in the literature that the Euclidean space controllability of the original system, robust with respect to a small parameter of singular perturbations, can be deduced from the controllability properties of the slow and fast systems. It also was established that such a connection between the controllability properties of the original system, and the slow and fast systems is valid only in a one direction. Namely, the controllability of the slow and fast systems yields the controllability of the original system, while the controllability of the original system not always yields the controllability of both slow and fast systems. In this paper, we consider the original system such that the respective fast system is uncontrollable, meaning that the previously established robust controllability conditions are not applicable for this original system. For this case, novel sufficient conditions of the robust Euclidean space controllability of the original system are derived. Illustrative examples are presented.