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On robustness against disturbances of passive systems with multiple invariant sets

Nelson Barroso 1 Rosane Ushirobira 1 Denis Efimov 1 Alexander Fradkov 2
1 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : Robustness of stability with respect to external perturbations is an important property characterizing the ability of the dynamics to counteract the influence of uncertainties. In the present paper such a property is investigated for the class of passive and strictly passive systems, which have several invariant compact and globally attracting subsets in the unforced scenario. It is assumed that the storage and supply rate functions are sign-definite with respect to these sets. The results are obtained within the framework of input-to-state stability and integral input-to-state stability for multistable systems. The robustness conditions are obtained for open-loop and for closed-loop cases, i.e. when an output feedback is required to guarantee robust-ness. Two applications (related with the model of multispecies populations) of the proposed theory are used to illustrate its efficiency.
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Submitted on : Saturday, March 28, 2020 - 12:12:53 PM
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Nelson Barroso, Rosane Ushirobira, Denis Efimov, Alexander Fradkov. On robustness against disturbances of passive systems with multiple invariant sets. International Journal of Systems, Control and Communications, Inderscience Publishers, In press, ⟨10.1080/00207179.2020.1750709⟩. ⟨hal-02523086⟩

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