Analytical solution of the Voznesenskiy problem for stationary and nonstationary linear systems

An exposition is made of the solution of the problem of decomposing and controlling the perturbed motion of a multiply connected system from the condition that autonomous subsystems with respect to each degree of freedom be asymptotically stable and possess a given spectrum. The decomposition algorithms are obtained in analytical form by the method of the inverse problems of dynamics. It is shown that the structure and the parameters of the algorithms are uniquely determined by the structure and the parameters of a mathematical model of the system being controlled and by the given spectrum of the models of the separate channels. The relationships between the algorithms of decomposition and control are written directly from the equations of motion of the system being decomposed and the standard models, with the aid of which the required dynamics of the autonomous subsystems is assigned. An examination is made of one-level and two-level structures. The solutions found are valid both for stationary and for nonstationary systems.