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A complementarity approach for the computation of periodic oscillations in piecewise linear systems

Abstract : Piecewise linear (PWL) systems can exhibit quite complex behaviours. In this paper, the com-plementarity framework is used for computing periodic steady-state trajectories belonging to linear time-invariant systems with PWL, possibly set-valued, feedback relations. The computation of the periodic solutions is formulated in terms of a mixed quadratic com-plementarity problem. Suitable anchor equations are used as problem constraints in order to determine the unknown period and to fix the phase of the steady-state oscillation. The accuracy of the complementarity problem solution is shown through numerical investigations of stable and unstable oscillations exhibited by practical PWL systems: a neural oscillator, a deadzone feedback system, a stick-slip system, a repressilator and a relay feedback system.
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https://hal.inria.fr/hal-02982668
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Submitted on : Thursday, October 29, 2020 - 4:02:17 PM
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Valentina Sessa, Luigi Iannelli, Francesco Vasca, Vincent Acary. A complementarity approach for the computation of periodic oscillations in piecewise linear systems. Nonlinear Dynamics, Springer Verlag, 2016, 85, pp.1255-1273. ⟨10.1007/s11071-016-2758-5⟩. ⟨hal-02982668v2⟩

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