Reconstructability of controlled switched linear systems: discrete and continuous states

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Abstract

© 2016, Springer-Verlag Berlin Heidelberg. This paper discusses the observability and reconstructability analysis of controlled switched linear systems. It is assumed that there is no information about the evolution of the discrete state neither it may be measured online. It is shown that, for the general case, observability of the discrete state does not depend on the observability of the continuous state and vice versa. Necessary and sufficient conditions are given under which a control input guarantees observability (reconstructability) of the discrete state. Corresponding results are obtained regarding the continuous state observability. Joining the obtained results, conditions are implied to guarantee the observability of the entire state (discrete and continuous). Finally, a mathematical algorithm is given describing a way to reconstruct both states.
Original languageAmerican English
Pages (from-to)1218-1230
Number of pages1094
JournalInternational Journal of Dynamics and Control
DOIs
StatePublished - 1 Sep 2018

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Switched Linear Systems
Observability
Linear systems
Joining
Entire
Necessary Conditions
Sufficient Conditions

Cite this

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title = "Reconstructability of controlled switched linear systems: discrete and continuous states",
abstract = "{\circledC} 2016, Springer-Verlag Berlin Heidelberg. This paper discusses the observability and reconstructability analysis of controlled switched linear systems. It is assumed that there is no information about the evolution of the discrete state neither it may be measured online. It is shown that, for the general case, observability of the discrete state does not depend on the observability of the continuous state and vice versa. Necessary and sufficient conditions are given under which a control input guarantees observability (reconstructability) of the discrete state. Corresponding results are obtained regarding the continuous state observability. Joining the obtained results, conditions are implied to guarantee the observability of the entire state (discrete and continuous). Finally, a mathematical algorithm is given describing a way to reconstruct both states.",
author = "Bejarano, {Francisco Javier}",
year = "2018",
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N2 - © 2016, Springer-Verlag Berlin Heidelberg. This paper discusses the observability and reconstructability analysis of controlled switched linear systems. It is assumed that there is no information about the evolution of the discrete state neither it may be measured online. It is shown that, for the general case, observability of the discrete state does not depend on the observability of the continuous state and vice versa. Necessary and sufficient conditions are given under which a control input guarantees observability (reconstructability) of the discrete state. Corresponding results are obtained regarding the continuous state observability. Joining the obtained results, conditions are implied to guarantee the observability of the entire state (discrete and continuous). Finally, a mathematical algorithm is given describing a way to reconstruct both states.

AB - © 2016, Springer-Verlag Berlin Heidelberg. This paper discusses the observability and reconstructability analysis of controlled switched linear systems. It is assumed that there is no information about the evolution of the discrete state neither it may be measured online. It is shown that, for the general case, observability of the discrete state does not depend on the observability of the continuous state and vice versa. Necessary and sufficient conditions are given under which a control input guarantees observability (reconstructability) of the discrete state. Corresponding results are obtained regarding the continuous state observability. Joining the obtained results, conditions are implied to guarantee the observability of the entire state (discrete and continuous). Finally, a mathematical algorithm is given describing a way to reconstruct both states.

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