Relative degree one and two sliding variables for multi-input discrete-time systems

In this paper we consider sliding mode control of multi-input discrete-time plants. For such plants, we propose the use of relative degree two sliding variables, which are known to improve robustness of single-input plants compared to their relative degree one equivalent. We investigate the design procedure of relative degree two sliding variables for multi-input systems. Then, we present two sliding mode control strategies obtained with the reaching law approach, using relative degree one and two sliding variables, respectively. We demonstrate that both reaching laws ensure desirable properties of the system sliding motion and that the method using relative degree two sliding variables ensures better robustness of the system than the one with relative degree one variables. We further show that the proposed reaching law based strategies enable independent tuning of individual inputs.