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Reconstructability of controlled switched linear systems: discrete and continuous states

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Abstract

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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Authors and Affiliations

  1. Instituto Politécnico Nacional, ESIME Ticomán, SEPI, Av. San José Ticomán 600, C.P. 07340, Mexico City, Mexico

    Francisco Javier Bejarano

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  1. Francisco Javier Bejarano
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Correspondence to Francisco Javier Bejarano.

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The author acknowledges the financial support of Proyecto SIP 20161492.

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Bejarano, F.J. Reconstructability of controlled switched linear systems: discrete and continuous states. Int. J. Dynam. Control 6, 1218–1230 (2018). https://doi.org/10.1007/s40435-016-0284-4

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  • DOI: https://doi.org/10.1007/s40435-016-0284-4

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