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On oscillations damping and control for a class of affine systems

The paper considers a class of continuous affine systems with oscillating behaviour due to the presence of pairs of complex eigenvalues in the spectrum of the system matrix. The control problem consists of damping the oscillations and tracking a piecewise constant reference signal. A control solution is proposed, based on pole placement combined with the internal model principle. Sufficient conditions for the controller existence are deduced and some issues concerning fixed and variable step simulations approaches are discussed. The results can be extended to piecewise affine hybrid systems, composed of a set of piecewise affine systems and a switching strategy based on a state space partition.