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Article Dans Une Revue Automatica Année : 2023

Graph-based conditions for feedback stabilization of switched and LPV systems

Résumé

This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the robust case, in which the active mode is completely unknown and unobservable, and ii) the mode-dependent case, in which the controller depends on the current active switching mode. The technical developments are based on graph-theory tools, relying in particular on the path-complete Lyapunov functions framework. The main idea is to use directed and labeled graphs to encode Lyapunov inequalities to design robust and mode-dependent piecewise linear state-feedback controllers. This results in novel and flexible conditions, with the particular feature of being in the form of linear matrix inequalities (LMIs). Our technique thus provides a first controller-design strategy allowing piecewise linear feedback maps and piecewise quadratic (control) Lyapunov functions by means of semidefinite programming. Numerical examples illustrate the application of the proposed techniques, the relations between the graph order, the robustness, and the performance of the closed loop.
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Dates et versions

hal-04137220 , version 1 (22-06-2023)
hal-04137220 , version 2 (15-01-2024)

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Matteo Della Rossa, Thiago Alves Lima, Marc Jungers, Raphaël Jungers. Graph-based conditions for feedback stabilization of switched and LPV systems. Automatica, 2023, 160, pp.111427. ⟨10.1016/j.automatica.2023.111427⟩. ⟨hal-04137220v2⟩
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