Stability and robustness of variable structure control system

By using eigenvalue perturbation theory, the stability and robustness of linear variable structure control (VSC) system were studied. The stability and robustness measures of closed-loop VSC system with mismatch parameters and input uncertainties were proposed. The stability margin means the maximum parameter perturbation range allowed by the closed-loop system to ensure stability, while robustness measures represent maximum variation range of the closed-loop VSC eigenvalues caused by unit norm of mismatch uncertainties. The relation between the stability and robustness and sliding mode design were analyzed. A sufficient condition of asymptotic stability for the closed-loop VSC system was provided.