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A complementarity approach for the computation of periodic oscillations in piecewise linear systems. (English) Zbl 1355.93076
Summary: Piecewise linear (PWL) systems can exhibit quite complex behaviours. In this paper, the complementarity 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 complementarity 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.

MSC:
93B52 Feedback control
34A36 Discontinuous ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
Software:
AUTO; PATH Solver; TC-HAT
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