Non-switching reaching law for sliding mode control of discrete time systems

In this paper we study the reaching law approach to the sliding mode control of discrete time linear dynamic systems. We propose a new non-switching type reaching law which determines the sliding variable decrease rate adjusted according to the current value of this variable. The reaching law introduced in this paper results in the quasi-sliding motion understood as remaining of the system state in a predefined vicinity of (band around) the sliding hyperplane. The reaching law does not cause chattering, i.e. it does not make the system state cross the hyperplane during the control process. The proposed reaching law guarantees fast convergence and offers good robustness with respect to modeling uncertainty and external disturbances.