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Adaptive robust control of uncertain time delay systems. (English) Zbl 1086.93029
Summary: The problem of adaptive robust control for uncertain linear systems with multiple delays occurring in the state variables is studied in this paper. The essential requirement for the uncertainties is that they satisfy matching conditions and are norm-bounded, but the bounds of the uncertainties are not necessarily known. An adaptive controller is developed based on linear matrix inequality technique and it is shown that the controller can guarantee the state variables of the closed loop system to converge, globally, uniformly and exponentially, to a ball in the state space with any pre-specified convergence rate. The effectiveness of our approach has been verified by its application in the control of river pollution process for the purpose of preserving standards of water constituents in streams.

##### MSC:
 93C40 Adaptive control/observation systems 93C23 Control/observation systems governed by functional-differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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