Stability of Nonstationary Automatic-Control Systems of Variable Structure in Forced Motion

Conditions of stability in sliding mode are obtained for nonstationary dynamic automatic-control processes of variable structure. The nonstationary parameters of a control process subjected to external perturbations vary in given ranges, whereas the parameters of the switching plane remain constant for the appropriately chosen parameters of discontinuous logic control laws. The corresponding system of differential equations contains coefficients that vary stepwise in time together with the parameters of the controlled process. The general stability criteria for the solutions of variable-structure systems are used to analyze the stability of motion in sliding mode of an automatic variable-structure control system of the second order