Preservation of the dissipativity properties of a class of nonsmooth dynamical systems with the (θ,γ)-algorithm

Scott Greenhalgh 1 Vincent Acary 1 Bernard Brogliato 1
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 sys- tems 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 so- lutions, and with state jumps are studied. The notion of numerical dissipation is given a rigorous meaning.
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Submitted on : Monday, May 30, 2011 - 4:28:10 PM
Last modification on : Thursday, February 7, 2019 - 5:28:41 PM
Long-term archiving on : Wednesday, August 31, 2011 - 2:27:30 AM

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Scott Greenhalgh, Vincent Acary, Bernard Brogliato. Preservation of the dissipativity properties of a class of nonsmooth dynamical systems with the (θ,γ)-algorithm. [Research Report] RR-7632, INRIA. 2011, pp.51. ⟨inria-00596961⟩

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