CONTROLLABILITY OF ESSENTIALLY VARIOUS-SPEED SINGULARLY PERTURBED DYNAMIC SYSTEMS

Abstract

The paper considers the controllability problem of essentially various-speed singularly perturbed dynamic system consisting of three subsystems of different dimensions, containing a small parameter to a variable degree as a multiplier for derivatives.   A method for studying complete and relative controllability of such systems has been proposed in the paper. The method is based on investigation of a controllability matrix rank. The matrix is composed of solution components of algebraic recurrent equations, which are drawn directly in accordance with the studied system of differential equations. The obtained effective algebraic conditions of controllability, expressed through parameters of the investigated system are obtained are illustrated by the case of essentially various-speed singularly perturbed dynamic system of fifth order with rational powers of small parameter