A new reaching law for discrete-time variable structure systems

Discrete time quasi-sliding mode control systems are considered. A definition describing the quasi-sliding mode as such a motion of the system that its state always remains in a vicinity of the sliding hyperplane is introduced. Then novel reaching laws satisfying conditions of the definition are proposed and applied to the design of linear control strategies which drive the state of the controlled system to a band around the sliding hyperplane. Consequently undesirable chattering is avoided. The strategies, when compared with previously published results, guarantee better robustness, faster error convergence and improved steady state accuracy of the system. Furthermore, better performance of the system is achieved using essentially reduced control effort