Control processes

On asymptotic behaviour of certian discrete delayed-control systems

A. V. Stepanov

D. I. Mendeleyev Institute for Metrology (VNIIM), 19, Moskovsky pr., St. Petersburg, 190005, Russian Federation

Abstract: Sufficient conditions are obtained for the existence of stable periodic or almost periodic solutions of some discrete delayed control systems based on solution roughness concept. Namely, by analogy with elemental case it is demonstrated that any rough solution of discrete delayed system with stable controlled object and piecewise constant control statement having finite codomain, tends in time to a stable periodic solution of that system (or almost periodic, if e. g. the delay sequence is almost periodic). Both cases when delay presents itself in controlled object and in control action are considered. A case is also considered when the control delay depends on previous system states. Bibliogr. 11.

Keywords: discrete control systems, delay, stability, periodic solutions, almost periodic solutions.

UDC: 681.511.42

Received: June 26, 2014

Language: English