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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 2 GIPSA-SYSCO - SYSCO GIPSA-DA - Département Automatique

Abstract : We consider the problem of stability in a class of differential equations which are driven by a differential measure associated with inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive Lyapunov-based conditions on the system-s vector fields for asymptotic stability under a specific class of inputs. These conditions are based on the stability margin of the Lebesgue-integrable and the measure-driven components of the system. For more general inputs which do not necessarily lead to asymptotic stability, we then derive conditions such that the maximum norm of the resulting trajectory is bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state stability in measure-driven systems.

Résumé : Cet article traite de systèmes commandés par des mesures, et leur stabiité.





Autor: Aneel Tanwani - Bernard Brogliato - Christophe Prieur -

Fuente: https://hal.archives-ouvertes.fr/



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