Robust sliding mode controllers design techniques for stabilization of multivariable time-delay systems with parameter perturbations and external disturbances

In this paper, robust delay-independent stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances are considered. To achieve this goal, two types of robust sliding mode controllers design techniques are advanced. The first is an integral sliding mode controller design modification to Shyu and Yan type controller design. The mismatching sliding conditions are parametrically obtained by using the Lyapunov-Razumikhin-Hale method and formulated in terms of some 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 is advanced by using the Lyapunov-Krasovskii V-functional method. The sliding, global stability and delay-dependent β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. A sliding mode controller design example for AV-8A Harrier VTOL aircraft with lateral unstable dynamic model parameters is considered to illustrate the controller design method. Design procedures and simulation results show that our advanced method is useful, and unstable lateral dynamics is successfully stabilized by using the combined controller.