On the stability of a program manifold of control systems with variable coefficients

Abstract

UDC 517.956
We study the absolute stability of the program manifold of basic control systems with variable coefficients and stationary nonlinearities. The conditions of stability of basic systems are investigated in a neighborhood of a given program manifold. The nonlinearities satisfy the conditions of local quadratic relationship. Sufficient conditions for the absolute stability of the program manifold with respect to a given vector function are established by constructing the Lyapunov function. A method used to select the Lyapunov matrix is specified.