Nonlinear and Hybrid Feedbacks with Continuous-Time Linear Systems

Cocetti, Matteo (2019) Nonlinear and Hybrid Feedbacks with Continuous-Time Linear Systems. PhD thesis, University of Trento, Institut National des Sciences Appliquées de Toulouse.

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In this thesis we study linear time-invariant systems feedback interconnected with three specific nonlinear blocks; a play/stop operator, a switching-reset mechanism, and an adaptive dead-zone. This setup resembles the Lure problem studied in the absolute stability framework, but the types of nonlinearities considered here do not satisfy (in general) a sector condition. These nonlinear blocks give rise to a whole range of interesting phenomena, such as compact sets of equilibria, hybrid omega-limit sets, and state constraints. Throughout the thesis, we use the hybrid systems formalism to describe these phenomena and to analyze these loops. We obtain sharp stability conditions that can be formulated as linear matrix inequalities, thus verifiable with numerically efficient solvers. Finally, we apply the theoretical findings to two automotive applications.

Item Type:Doctoral Thesis (PhD)
Doctoral School:Materials, Mechatronics and Systems Engineering
PhD Cycle:31
Subjects:Area 09 - Ingegneria industriale e dell'informazione > ING-INF/04 AUTOMATICA
Repository Staff approval on:23 May 2019 10:14

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