Calming the solution of systems of neutral type with many delays using feedback

A. V. Metel'skii ; V. E. Khartovskii ; O. I. Urban

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2014), pp. 40-51

Résumé

This paper examines the following problem: a linear autonomous differential-difference system of neutral type with delay in state requires ensuring its complete calming by feedback. To solve this problem linear autonomous dynamic differential-difference controller with state feedback is proposed; this controller does not exclude a closed system from the original class of linear autonomous systems of neutral type. Sufficient condition for the existence of such a controller coincides with the criterion of complete controllability. In addition, the closed system has a finite spectrum, which simplifies greatly the problem of calculating the current state during the technical implementation of the controller. The basic idea of research is to select parameters for the controller so that the closed system becomes point-degenerated in directions corresponding to phase components of the original (open) system. To do this, the original system is first converted via feedback to the single-input system of retarded type. Further, for the resulting object the dynamic controller that provides the degeneracy of the corresponding phase components is constructed. The proposed procedure for constructing the control action is based on the algebraic properties of shift operator and does not involve calculating the roots of characteristic quasipolynomial of the original system. It can be used to provide full calming as well as exponential stability to a closed system. However, in the latter case it is necessary to use dynamic controller with state feedback of integral type.

Détail

Keywords: difference-differential system, neutral type, complete controllability, controller, feedback, point degeneration.