Sliding mode control of time delay systems - A non-switching type reaching law approach

In this paper we consider a relatively simple, but fairly important from practical point of view class of time delay systems and we analyze the possibility of applying sliding mode control to steer them. The systems under consideration consist of a single integrator with multiple, parallel delays in the input channel. Since (due to delays and mismatched disturbance) direct application of the sliding mode paradigm to these systems is not feasible, we propose a new discrete time sliding mode controller. In order to obtain fast reaction of the systems to the unpredictable disturbance, the controller employs an appropriately selected sliding hyperplane. Moreover, as we require input signal constraints to be satisfied, the controller design is performed with the use of a new non-switching type reaching law. Application of the reaching law results in chattering free sliding motion and improved robustness with respect to external disturbance when compared with earlier designs.