Design of adaptive variable structure controllers for perturbed time-varying state delay systems

The problem of stabilizing a class of perturbed linear dynamic systems with time-varying state delay is investigated in this paper. By applying the Lyapunov stability theorem, we develop a delay-independent adaptive variable structure controller to drive the states of system to zero. Based on the variable structure control (VSC) technique, the proposed controller can drive the system into a pre-specified sliding hyperplane to obtain the desired dynamic performance. Once the dynamics of system reach the sliding plane, the proposed controlled system is insensitive to perturbations. The use of adaptive technique is to overcome the unknown upper bound of perturbations so that the reaching condition (or sliding condition) can be satisfied. Furthermore, the globally asymptotic stability is guaranteed for the proposed control scheme under certain conditions. Finally, an example is given to illustrate the feasibility of the proposed control methodology.