Finite-time sliding mode control of switched systems with one-sided Lipschitz nonlinearity

Abstract This work investigates the problem of input-output finite-time stability (IO-FTS) for one-sided Lipschitz switched systems by sliding mode control (SMC) approach. A key issue is how to ensure the IO-FTS of the switched systems during the whole finite-time interval under the unknown one-sided Lipschitz nonlinearity. To this end, a sliding mode law is constructed to ensure the the state trajectories can be driven onto the sliding surface during the assigned finite time interval. By means of partitioning strategy and the multiple Lyapunov function (MLF) approach, the corresponding IO-FTS over reaching phase and sliding motion phase are guaranteed, respectively. And then, some sufficient conditions are derived by utilizing the one-sided Lipschitz and quadratically inner-bounded conditions. Finally, an illustrative example is given to illustrate the proposed method.