Discrete time sliding mode control in the presence of state and control signal constraints

In this paper we consider the discrete time sliding mode control of the plant perturbed by the unknown, bounded external disturbances. The controller is designed using the reaching law approach. This method allows us to better control the systems dynamics up to the sliding phase. The rate of convergence of the sliding variable to zero is chosen in such a manner to ensure the fulfillment of the given constraints on the system state and the control signal. The properties of the proposed sliding mode controller are demonstrated analytically and in computer simulations.