Observer-Based Sliding Mode Control for Stabilization of Mismatched Disturbance Systems With or Without Time Delays

In this article, the stabilization problem of mismatched disturbance systems with or without time delays is studied via observed-based sliding mode control (SMC). Two kinds of SMC schemes for systems with time delay and without time delay are considered, respectively. When time delay is addressed in the system, an SMC strategy is structured via disturbance observer, where the unknown external disturbances are supposed to be generated by an exogenous dynamic. When time delay is not addressed, an SMC approach is designed in which the unknown external disturbances are assumed to tend to a constant steady state in infinite time. Sufficient conditions for stability of the corresponding sliding motion are derived by using Lyapunov–Krasovskii functional and Lyapunov function approach, respectively. Our results can be applied when the bound of the disturbances are unmeasured or unknown. Two simulation examples are shown to illustrate the proposed methods.