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Balanced truncation for linear switched systems

Abstract : We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians.
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https://hal.inria.fr/hal-01832883
Contributor : Christophe Fiter <>
Submitted on : Tuesday, September 11, 2018 - 6:06:55 PM
Last modification on : Friday, December 11, 2020 - 6:44:07 PM
Long-term archiving on: : Wednesday, December 12, 2018 - 4:33:12 PM

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Ion Victor Gosea, Mihaly Petreczky, Athanasios C. Antoulas, Christophe Fiter. Balanced truncation for linear switched systems. Advances in Computational Mathematics, Springer Verlag, 2018, ⟨10.1007/s10444-018-9610-z⟩. ⟨hal-01832883⟩

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