Robust sliding mode control of multivariable time-delay systems

In this paper, robust stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances is considered. To achieve this goal two types of robust sliding mode controller design techniques are advanced. The first one is an integral sliding mode controller design modification to Shyu and Yan type controller design. By using the Lyapunov-Razumikhin-Hale method the mismatching sliding conditions are parametrically obtained and formulated in terms of matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations are advanced by using Lyapunov-Krasovskii V-functional method. The sliding, global stability and β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. Numerical examples with simulation results show the effectiveness of design procedures.