MIMO sliding mode controller design using inverse hyperbolic function

In this work a new reaching law (RL) is proposed that uses inverse hyperbolic function (IHF) instead of the Signum function for switching. The characteristic of this reaching law is that its switching gain is variable, during the reaching phase, which is governed by the parameters of IHF. Its gain decreases with the convergence of system states towards the sliding surface. The variable gain results in: (a) the considerable reduction of the phenomenon of chattering at the control inputs and (b) the decrease of the reaching phase of the sliding mode control (SMC).