Abstract
In this paper we study the property of state-trimness introduced in [4], which, together with observability, is a necessary and sufficient condition for the minimality of the state-space realizations of a given input-output behavior. More concretely, we show how to compute the trim subspace \(\mathcal T\) of a non state-trim state-space system \(\varSigma \) and prove that the restriction of \(\varSigma \) to \(\mathcal T\) is a state-space system with the same input-output behavior as \(\varSigma \). Combined with Kalman’s observability decomposition, this allows obtaining minimal state-space realizations from non minimal ones.
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Acknowledgement
This work is supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UIDB/04106/2020. Moreover, it was also partially supported by Base Funding - UIDB/00147/2020 and Programmatic funding - UIDP/00147/2020 of the Systems and Technologies Center - SYSTEC - funded by national funds through the FCT/MCTES (PIDDAC).
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Pereira, R., Rocha, P. (2022). A New Insight on State-Trimness and Minimal State-Space Realizations of Input-Output Behaviors. In: Brito Palma, L., Neves-Silva, R., Gomes, L. (eds) CONTROLO 2022. CONTROLO 2022. Lecture Notes in Electrical Engineering, vol 930. Springer, Cham. https://doi.org/10.1007/978-3-031-10047-5_60
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DOI: https://doi.org/10.1007/978-3-031-10047-5_60
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