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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.

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
Full Text: DOI
[1] Corless, M.; Leitmann, G., Bounded controllers for robust exponential convergence, Journal of optimization theory and applications, 76, 1-12, (1993) · Zbl 0791.93022
[2] Foda, S.G.; Mahmoud, M.S., Adaptive stabilization of delay differential systems with unknown uncertainty bounds, International journal of control, 71, 259-275, (1998) · Zbl 0965.93093
[3] Ichikawa, K., Adaptive control of delay systems, International journal of control, 43, 1653-1659, (1986) · Zbl 0612.93039
[4] Lee, C.S.; Leitmann, G., Continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems: an application to river pollution control, Computers and mathematics with applications, 16, 929-938, (1988) · Zbl 0673.93052
[5] Mahmoud, M.S., Adaptive control of a class of time-delay systems with uncertain parameters, International journal of control, 63, 937-950, (1996) · Zbl 0847.93055
[6] Nihtila, M.T., Adaptive control of a continuous-time system with time-varying input delay, Systems and control letters, 12, 357-364, (1989) · Zbl 0669.93050
[7] Ortega, R.; Lozano, R., Globally stable adaptive controller for systems delay, International journal of control, 47, 17-23, (1988) · Zbl 0646.93039
[8] Oucheriah, S., Adaptive robust control of a class of dynamic delay systems with unknown uncertainty bounds, International journal of adaptive control and signal processing, 15, 53-63, (2001) · Zbl 0982.93066
[9] Tao, G., Model reference adaptive control of multivariable plants with delays, International journal of control, 55, 393-414, (1992) · Zbl 0748.93056
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