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Existence of Reachable and Observable Triples of Linear Discrete-Time Descriptor Systems

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Abstract

This work studies the reachability and observability of discrete-time descriptor systems and considers the following problem: Given a matrix pair (E, A), find a matrix B (C) such that the corresponding descriptor system is not reachable (observable). The computation of such a matrix can give us a set of conditions that can then be taken into account when constructing the matrix B (C) to make the system reachable (observable). The above problem is solved by working on the equivalent causal and noncausal subsystems that are obtained through the Weierstrass decomposition of discrete-time descriptor systems. Positive descriptor systems are also considered. The developed theory is illustrated through physical and numerical examples.

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Acknowledgements

The authors are grateful to the anonymous reviewers for their constructive comments to improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Lazaros Moysis

  2. The Logistics Institute - Asia Pacific, National University of Singapore, Singapore, 119613, Singapore

    Vikas Kumar Mishra

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  1. Lazaros Moysis
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  2. Vikas Kumar Mishra
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Correspondence to Vikas Kumar Mishra.

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Moysis, L., Mishra, V.K. Existence of Reachable and Observable Triples of Linear Discrete-Time Descriptor Systems. Circuits Syst Signal Process 38, 1086–1098 (2019). https://doi.org/10.1007/s00034-018-0922-5

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  • DOI: https://doi.org/10.1007/s00034-018-0922-5

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