Computing Period and Shape of Oscillations in Piecewise Linear Lur'e Systems: a Complementarity Approach

Valentina Sessa 1 Luigi Iannelli 1 Vincent Acary 2, * Bernard Brogliato 2 Francesco Vasca 1
* Corresponding author
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Autonomous piecewise linear systems in the Lur'e form may exhibit periodic steady-state oscillations. For many practical systems belonging to this class the period and the shape of the oscillation is difficult to be predicted a priori. In this paper the complementarity approach is used to tackle the issue. The complementarity formalism is used to represent the closed-loop system and a phase condition acting as an anchor equation for the periodic solution. By discretizing the dynamics a mixed complementarity problem is formulated. The corresponding solution provides an accurate prediction of the steady-state oscillation and its period. Numerical results show the effectiveness of the proposed technique for the computation of stable and sliding periodic solutions. The analysis of the steady-state solution of a Colpitts oscillator is considered as an illustration.
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Valentina Sessa, Luigi Iannelli, Vincent Acary, Bernard Brogliato, Francesco Vasca. Computing Period and Shape of Oscillations in Piecewise Linear Lur'e Systems: a Complementarity Approach. CDC 2013 - 52nd IEEE Conference on Decision and Control, Dec 2013, Firenze, Italy. pp.4680-4685, ⟨10.1109/CDC.2013.6760622⟩. ⟨hal-00870282⟩

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