Stability analysis of sliding-mode feedback control

This paper provides new analytic tools leading to the first rigorous stability and robustness analysis of sliding-mode feedback controllers. Unrestrictive conditions are given, under which these controllers are stabilizing in the presence of large disturbances, as well as modeling, actuator and observation errors. The stability conditions invoke the existence of two Lyapunov-type functions, the first associated with passage to the sliding set in finite time, and the second with convergence to the desired state. In this approach, account is taken, from the outset, of implementational constraints. We provide a framework for establishing stability and robustness of the closed-loop system, for a variety of implementation schemes. We illustrate our results by means of two examples of the type frequently encountered in the sliding-mode literature.