Program motions stabilization of variable structure systems

The program motions orbital stabilization problem is considered for systems with piecewise constant controls. The problem is reduced to the elucidation of the linear difference equations special system asymptotic stability. The considered systems class, called variable-structure systems, is included in the so-called transforming systems class, which are currently growing interest in the present time. An orbital stability criterion and a desired stabilizing control synthesizing method for the structurally linear systems in the case of auto-oscillation constructions are proposed.