State feedback sliding mode control of a class of uncertain time delay systems

The robust stability of a class of uncertain systems involving internal delays while being regulated by a sliding mode controller (SMC) is studied. The method for designing a SMC is proposed for the generation of a sliding motion in the system. The robustness property and asymptotic stability of the system are discussed and conditions for the design of the switching hyperplane are given. Further generalisation results, which lead to a simple design and implementation, are made for the case when the system is in companion form. A method is proposed for the elimination of limit cycles in systems being regulated by a relay SMC while allowing the generation of sliding motion and thus ensuring the closed-loop asymptotic stability.