A new LMI-based robust Sliding Mode Control for the uncertain discrete-time systems

Abstract

Abstract-In this paper, a new approach for designing a robust Discrete-time Sliding Mode Control (DSMC) is proposed for the uncertain discrete-time systems. To this end, an LMI approach is used to develop a new framework to design the linear sliding functions which are linear to the state. The LMI approach proposed in this paper is designed to deal with uncertain systems (matched and unmatched). It is wellknown that the finite sampling rate for the discrete-time systems leads to this fact that state move within a bound around the predetermined sliding surface referred to as quasi-sliding mode band. In this paper, this matter will be discussed in a new point of view and an innovative method will be used to obtain the ultimate bound on the system state.

Discrete higher order sliding mode: concept to validation

“…Assumption 1 The disturbance vector is matched, i.e. , where represents the unmodelled dynamics and the external disturbance effect in the system. Assumption 2 is bounded and its constant bounds are known. Remark 2 In the literature of sliding mode, generally the effect of unmodelled dynamics and external disturbance are assumed to be bounded by a constant [24]. This assumption is not very conservative as a large class of systems fall into this category [25].…”