Narrow Results

In this paper we announce a new framework for a rigorous stability analysis of sliding-mode controllers. We give unrestrictive conditions under which such feedback controllers are robustly stabilizing. These conditions make allowance for large disturbance signals, for modeling, actuator and observation measurement errors, and also for the effects of digital implementation of the control. The proposed stability analysis techniques involve two Lyapunov-type functions. The first is associated with passage to the sliding surface in finite time; the second, with convergence to the state associated with the desired equilibrium point. Application of the techniques is illustrated with reference to higher-order linear systems in control canonical form.