Regulation of Linear Systems with Unknown Additive Sinusoidal Sensor Disturbances

Known linear stabilizable and detectable systems, which are allowed to be non minimum phase, are considered: the problem of tracking unknown output reference trajectories and rejecting unknown input disturbances when the output tracking error is affected by unknown additive sensor disturbances is addressed. All the exogenous signals to be tracked and/or to be rejected are assumed to be the sum of sinusoids: only upper bounds on their numbers are supposed to be known, along with a set in which the output disturbance frequencies may range. A constructive algorithm is proposed to drive the regulation error exponentially to zero. The regulation strategy includes an on-line detector of the number of excited frequencies and exponentially converging estimates of the exosystems parameters. An example containing a variable number of frequencies is worked out and simulated.

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