1. Stabilisation of discrete‐time systems with finite‐level uniform and logarithmic quantisers
- Author
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Carlos Eduardo Pereira, Sophie Tarbouriech, Gustavo Cruz Campos, João Manoel Gomes da Silva, Departamento de Engenharia Eletrica (UFRGS), Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)
- Subjects
0209 industrial biotechnology ,Control and Optimization ,Logarithm ,020208 electrical & electronic engineering ,Linear system ,Linear matrix inequality ,Admissible set ,02 engineering and technology ,State (functional analysis) ,[SPI.AUTO]Engineering Sciences [physics]/Automatic ,Computer Science Applications ,Human-Computer Interaction ,020901 industrial engineering & automation ,Discrete time and continuous time ,Control and Systems Engineering ,Control theory ,Attractor ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Electrical and Electronic Engineering ,Mathematics - Abstract
International audience; This study deals with the stabilisation of discrete-time linear systems subject to static finite-level quantisation on thecontrol inputs. Two kinds of quantisers are considered: uniform and logarithmic. The modelling of the finite-level quantisation isobtained by the application of deadzone and saturation maps to an infinite-level quantiser. From this model, conditions for thesynthesis of state feedback control laws guaranteeing the convergence of the trajectories to an attractor around the originprovided that the initial state belongs to a certain admissible set are proposed. These conditions can thus be incorporated inlinear matrix inequality-based optimisation schemes to compute the stabilising gain while minimising the size of the attractor.
- Published
- 2018
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