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Characterizations of global reachability of 2D structured systems

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Abstract

The new concept of 2D structured system is defined and characterizations of global reachability are obtained. This paper extends well known results for the 1D case, according to which a structured system (A λ, B λ) is (generically) reachable if and only if its graph is spanned by a cactus, or, equivalently, if and only if the pair (A λ, B λ) is full generically row rank and irreducible.

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References

  • Davison E. J., Wang S.-H. (1973) Properties of linear time-invariant multivariable systems subject to arbitrary output and state feedback. IEEE Transactions on Automatic Control 18: 24–32

    Article  MathSciNet  MATH  Google Scholar 

  • Dion J.-M., Commault C., van der Woude J. (2003) Generic properties and control of linear structured systems: A survey. Automatica 39(7): 1125–1144

    Article  MathSciNet  MATH  Google Scholar 

  • Fornasini E., Marchesini G. (1978) Doubly-indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory 12: 59–72

    Article  MathSciNet  MATH  Google Scholar 

  • Glover K., Silverman L. (1976) Characterization of structural controllability. IEEE Transactions on Automatic Control 21: 534–537

    Article  MathSciNet  MATH  Google Scholar 

  • Kučera, V. (1991). Analysis and design of discrete linear control systems. Prentice Hall International Series in Systems and Control Engineering. New York: Prentice Hall.

  • Lin C.-T. (1974) Structural controllability. IEEE Transactions on Automatic Control 19: 201–208

    Article  MATH  Google Scholar 

  • Mayeda H. (1981) On structural controllability theorem. IEEE Transactions on Automatic Control 26: 795–798

    Article  MathSciNet  MATH  Google Scholar 

  • Shields R. W., Pearson J. (1976) Structural controllability of multiinput linear systems. IEEE Transactions on Automatic Control 21: 203–212

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Aveiro, Campus de Santiago, 3810-193, Aveiro, Portugal

    Ricardo Pereira & Rita Simões

  2. Department of Electrical and Computer Engineering, Faculty of Engineering, University of Oporto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    Paula Rocha

Authors
  1. Ricardo Pereira
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  2. Paula Rocha
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  3. Rita Simões
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Corresponding author

Correspondence to Ricardo Pereira.

Additional information

This work was partially supported by FCT–Fundação para a Ciência e Tecnologia through CIDMA–Centro de Investigação e Desenvolvimento em Matemática e Aplicações of the University of Aveiro, Portugal.

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Pereira, R., Rocha, P. & Simões, R. Characterizations of global reachability of 2D structured systems. Multidim Syst Sign Process 24, 51–64 (2013). https://doi.org/10.1007/s11045-011-0154-3

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  • DOI: https://doi.org/10.1007/s11045-011-0154-3

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