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Output feedback stabilization of linear systems with unknown additive output sinusoidal disturbances. (English) Zbl 1360.93559
Summary: The output feedback exponential stabilization problem is addressed for known linear stabilizable and detectable systems when the measured output is affected by sinusoidal disturbances generated by an unknown exosystem and only an upper bound on the exosystem order is supposed to be known. Necessary and sufficient conditions are given: in particular a solution to the problem exists if and only if the set of exosystem eigenvalues is disjoint from the set of system eigenvalues. Two adaptively stabilizing control algorithms are proposed: the first one drives the state of the given system exponentially to zero when the actual disturbances are exactly modeled by the exosystem. When the exosystem overmodels the actual disturbances, an online detector of the number of excited frequencies is included in the second more complex algorithm: the exponentially converging estimates of the system state variables are then used to drive the state of the given system exponentially to zero. An illustrative example with a disturbance containing a variable number of frequencies is worked out in details and simulated.

MSC:
93D15 Stabilization of systems by feedback
93C73 Perturbations in control/observation systems
93B35 Sensitivity (robustness)
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