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 Ly apunov stability theorem, we develop a delay-independent adaptive variable structure controller to drive the states of system to zero. Based on the va riable structure control (VSC) technique, the proposed controller can drive the system into a pre-specified sliding hyperplane to obtain the desired d ynamic performance. Once the dynamics of system reach the sliding plane, th e proposed controlled system is insensitive to perturbations. The use of ad aptive technique is to overcome the unknown upper bound of perturbations so that the reaching condition (or sliding condition) can be satisfied. Furth ermore, the globally asymptotic stability is guaranteed fur the proposed co ntrol scheme under certain conditions. Finally, an example is given to illu strate the feasibility of the proposed control methodology. (C) 2001 The Fr anklin Institute. Published by Elsevier Science Ltd. All rights reserved.