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# Implicit Euler numerical simulations of sliding mode systems

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : In this report it is shown that the implicit Euler time-discretization of some classes of switching systems with sliding modes, yields a very good stabilization of the trajectory and of its derivative on the sliding surface. Therefore the spurious oscillations which are pointed out elsewhere when an explicit method is used, are avoided. Moreover the method (an event-capturing, or time-stepping algorithm) allows for accumulation of events (Zeno phenomena) and for multiple switching surfaces (i.e., a sliding surface of codimension $\geq 2$). The details of the implementation are given, and numerical examples illustrate the developments. This method may be an alternative method for chattering suppression, keeping the intrinsic discontinuous nature of the dynamics on the sliding surfaces. Links with discrete-time sliding mode controllers are studied.
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Cited literature [54 references]

https://hal.inria.fr/inria-00374840
Contributor : Vincent Acary Connect in order to contact the contributor
Submitted on : Friday, April 10, 2009 - 8:37:47 AM
Last modification on : Monday, April 25, 2022 - 8:46:09 AM
Long-term archiving on: : Wednesday, September 22, 2010 - 12:04:52 PM

### Files

RR-6886.pdf
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### Identifiers

• HAL Id : inria-00374840, version 2
• ARXIV : 0904.1682

### Citation

Vincent Acary, Bernard Brogliato. Implicit Euler numerical simulations of sliding mode systems. [Research Report] RR-6886, INRIA. 2009, pp.39. ⟨inria-00374840v2⟩

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