ANTIPERIODIC MOTIONS AND AN ALGEBRAIC CRITERION FOR THE ABSOLUTE STABILITY OF NONLINEAR TIME-VARYING SYSTEMS IN THE 3-DIMENSIONAL CASE

It is established that in third-order systems, for a boundary value of the parameter k, defining the variation sector of the nonlinear characteristic in the absolute stability problem, there occur antiperiodic motions having two switchings of the control over a half-period. A similar result has been established in 1971 for second-order systems [1]. In [2] one has proved the existence of periodic motions at an absolute stability bound in three-dimensional systems, but no estimate has been established for the number of switching points of the control in a period. A refinement of the result of [2], contained in this paper, solves completely M. A. Aizerman's problem in the form of an algebraic criterion for the indicated class of systems.