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Design of adaptive variable structure controllers for perturbed time-varying state delay systems. (English) Zbl 0966.93101
A class of continuous-time uncertain linear systems with time delay is considered. Based on a suitable Lyapunov function, a variable structure control strategy is proposed. Under suitable assumptions, this strategy guarantees globally asymptotic stability of the closed-loop system. The proposed strategy is composed of three parts: a linear state feedback part, a nonlinear switching part and an adaptive part. The use of the adaptive technique allows to overcome the unknown upper bound of the perturbations so that the sliding condition can be satisfied. An illustrative example and the corresponding computer simulations are also presented.

MSC:
93D21 Adaptive or robust stabilization
93B12 Variable structure systems
93C23 Control/observation systems governed by functional-differential equations
Software:
LMI toolbox
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