Characterizations of output controllability for LTI systems
| Autor: | Danhane, Baparou, Lohéac, Jérôme, Jungers, Marc |
|---|---|
| Přispěvatelé: | Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Lohéac, Jérôme |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Kalman rank condition
LTI systems minimal norm control [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] state to output controllability Gramian [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS] Hautus test [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] output controllability continuous and discrete time systems |
| Popis: | The objective of this paper is to make, in a simple and rigorous way, some contributions to the notion of output controllability. We first examine, for Linear Time-Invariant systems, the notion of state to output controllability, introduced in the 60s by Bertram and Sarachik. More precisely, we extend the Hautus test, well-known in the case of state controllability, to state to output controllability, and propose a controllability Gramian matrix, allowing us to build a continuous control achieving a transfer with minimal energy. We also give two other notions of output controllability, namely output to output and globally output to output controllability. For each of these two new notions, we give necessary and sufficient conditions, in terms of Kalman rank, Hautus test and Gramian matrices. All of these results are given in the framework of continuous time and discretized time systems. These results are illustrated by several numerical examples. |
| Databáze: | OpenAIRE |
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