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Continuous Dynamics Distinguishability

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H-Systems

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

In this chapter, we analyze the possibility of determining the current discrete state of an LH-system by using only the continuous output information. The identification of the discrete mode of a hybrid system corresponds to understanding which continuous dynamical system is evolving. The main role in the solution to this problem is played by the notion of distinguishability of a pair of dynamical systems, i.e. the possibility of inferring on the basis of the continuous output information which of the two systems is indeed active. This property is characterized in terms of input–output behavior. Always using the continuous information, we investigate the possibility of determining only the switching times, not the complete information about which discrete mode is active. Algorithmic tools are provided for the reconstruction of the current evolving system, in the continuous and discrete time domain. The analysis is extended to the case of discrete time systems with output corrupted by external malicious attacks on sensors.

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Notes

  1. 1.

    In our setting, the state dimension is the same for all the involved linear systems. The results on distinguishability also hold if the state dimensions of the given systems are not the same, since, as it will be seen, the necessary and sufficient conditions for distinguishability are based on the systems’ input-output responses.

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Authors and Affiliations

  1. Department of Information Engineering, Computer Science and Mathematics (DISIM), University of L’Aquila, Center of Excellence for Research DEWS, L’Aquila, Italy

    Elena De Santis & Maria Domenica Di Benedetto

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  1. Elena De Santis
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  2. Maria Domenica Di Benedetto
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Correspondence to Elena De Santis .

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De Santis, E., Di Benedetto, M.D. (2023). Continuous Dynamics Distinguishability. In: H-Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-20447-0_7

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