Discrete sliding mode control for time-varying delay systems: a multi-delay approach

Owing to its potential for real applications, many researchers have studied the problem of modelling and control of time-varying delay systems. In this paper, we propose a new strategy called multi-delay approach for modelling and control of these systems. In this new strategy, the time-varying delay systems are modelled by a multi-delay model representation in which each elementary model is characterised by a constant delay value varying between the lower and upper bounds of the delay term supposed to be known. A systematic elementary model reproducing the real output evolution is generated. Then, a discrete sliding mode control based on the multi-delay model representation (MD-DSMC) was developed to stabilise such systems. The proposed controller guarantees a finite time convergence of systems under consideration. The controller parameters are selected by solving linear matrix inequalities (LMIs). A comparative study with the classical discrete sliding mode control was also subject of this work.