On preserving dissipativity properties of linear complementarity dynamical systems with the $θ$-method

Scott Greenhalgh 1 Vincent Acary 1, * Bernard Brogliato 1
* Corresponding author
1 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 : In this work we study the following problem: given a numerical method (an extended $θ$−method named the ($θ,γ$)-method), find the class of dissipative linear complementarity systems such that their discrete-time counterpart is still dissipative, with the same storage (energy) function, supply rate (reciprocal variables), and dissipation function. Systems with continuous solutions, and with state jumps are studied. The notion of numerical dissipation is given a rigorous meaning.
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Scott Greenhalgh, Vincent Acary, Bernard Brogliato. On preserving dissipativity properties of linear complementarity dynamical systems with the $θ$-method. Numerische Mathematik, Springer Verlag, 2013, 125 (4), pp.601-637. ⟨10.1007/s00211-013-0553-5⟩. ⟨hal-00807807⟩

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