Multirate Output Feedback Based Discrete-Time Sliding Mode Control for a Class of Nonlinear Systems

The concept of sliding mode control was first introduced by Emelyanov [Emelyanov, 1967] and Utkin [Utkin, 1977]. It is a technique that achieves desired characteristics for the system by confining its states to a specified subset of the state space. This is done by application of a control of variable structure. The main advantage of sliding mode control is its insensitivity to system parameter variations [Hung et al., 1993,Young et al., 1999]. In the recent years, considerable efforts have been put in the study of the concepts of Digital Sliding Mode (DSM) controller design [Furuta, 1990, Gao et al., 1995, Sarpturk et al., 1978]. In case of the DSM design, the control input is applicable only at certain sampling instants and the control effort is constant over the entire sampling period. Moreover, when the states reach the switching surface, the subsequent control would be unable to keep the states confined to the surface. As a result, DSM can undergo only quasi-sliding mode, i.e., the system states would approach the sliding surface but would generally be unable to stay on it. Thus, in general, DSM does not possess the invariance property found in continuous-time sliding mode. In [Gao et al., 1995] a “reaching law” approach for the design of control for DSM using state feedback was introduced. This reaching law ensures that the system trajectory will hit the switching manifold and thereafter undergo a zigzag motion about the switching manifold. The magnitude of each successive zigzagging step decreases so that the trajectory stays within a specified band called the quasi-sliding-mode band.