Sliding Mode Control of Nonlinear Systems with Time-varying Delay

This paper considers a sliding mode control of multivariable nonlinear systems with time-varying delays.In our previous work, a sliding mode control design method combining with the finite spectrum assignment has been developed. In the design method, the sliding surface is constructed by using a coordinates transformation containing past values of the state variables. In most practical systems, however, it is difficult to identify exactly the length of time-delay.In this paper, we discuss the effect of uncertainties in time-delay and parameters on system's behaviour in the sliding modeand derive a sufficient condition to guarantee asymptotic stability for the systems in the sliding mode by using Lyapunov-Razumikhin function approach. Effectiveness of the proposed method is tested by an numerical simulation of continuous stirred-tank reactor (CSTR) system.