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Adaptive stabilization with exponential decay. (English) Zbl 0699.93071

Summary: Adaptive high gain stabilizers for classes of linear time-invariant state space systems are presented. The classes cover multi-input-multi-output systems where the state dimension is not known. Only standard assumptions such as minimum phase and known respectively unknown sign are required. The main result is, that the adaptive control laws of C. I. Byrnes and J. C. Willems [“Adaptive stabilization of multivariable linear systems”, Proc. 23rd IEEE Conf., Decis. Control, Las Vegas/NV 1984, Vol. 3, 1574-1577 (New York 1984)] can be modified to produce a guarantee of exponentially decaying states.

MSC:

93D15 Stabilization of systems by feedback
93C40 Adaptive control/observation systems
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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[1] Byrnes, C. I.; Willems, J. C., Adaptive stabilization of multivariable linear systems, (Proc. of the 23rd Conf. on Decision and Control. Proc. of the 23rd Conf. on Decision and Control, Las Vegas, NV (1984)), 1574-1577
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