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Detectability, Observability, and Asymptotic Reconstructability of Positive Systems

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Positive Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 389))

Abstract

We give a survey of detectability, observability and reconstructability concepts for positive systems and sketch some applications to the analysis of stochastic equations.

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References

  1. Berman, A., Neumann, M., Stern, R.: Nonnegative Matrices in Dynamic Systems. John Wiley and Sons Inc., New York (1989)

    MATH  Google Scholar 

  2. Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. In: Classics in Applied Mathematics, vol. 9. SIAM Publications, Philadelphia (1994)

    Google Scholar 

  3. Costa, E., do Val, J.: On the detectability and observability of discrete-time Markov jump linear systems. Syst. Control Lett. 44(2), 135–145 (2001)

    Article  MATH  Google Scholar 

  4. Costa, E., do Val, J., Fragoso, M.: A new approach to detectability of discrete-time infinite Markov jump linear systems. SIAM J. Control Optim. 43(6), 2132–2156 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Da Prato, G., Ichikawa, A.: Stability and quadratic control for linear stochastic equations with unbounded coefficients. Boll. Unione Mat. Ital., VI. Ser., B 6, 987–1001 (1985)

    Google Scholar 

  6. Damm, T.: Stability of linear systems and positive semigroups of symmetric matrices. In: Benvenuti, L., Santis, A.D., Farina, L. (eds.) Positive Systems. LNCIS, vol. 294, pp. 207–214. Springer, Heidelberg (2003)

    Google Scholar 

  7. Damm, T.: Rational Matrix Equations in Stochastic Control. LNCIS, vol. 297. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  8. Damm, T.: On detectability of stochastic systems. Automatica 43(5), 928–933 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Drǎgan, V., Halanay, A., Stoica, A.: A small gain theorem for linear stochastic systems. Syst. Control Lett. 30, 243–251 (1997)

    Article  Google Scholar 

  10. Drǎgan, V., Morozan, T.: Stochastic observability and applications. IMA J. Math. Control & Information 21(3), 323–344 (2004)

    Article  Google Scholar 

  11. Elsner, L.: Quasimonotonie und Ungleichungen in halbgeordneten Räumen. Linear Algebra Appl. 8, 249–261 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fragoso, M.D., Costa, O.L.V., de Souza, C.E.: A new approach to linearly perturbed Riccati equations in stochastic control. Appl. Math. Optim. 37, 99–126 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Freiling, G., Hochhaus, A.: On a class of rational matrix differential equations arising in stochastic control. Linear Algebra Appl. 379, 43–68 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Härdin, H.M., Van Schuppen, J.H.: Observers for linear positive systems. Linear Algebra Appl. 425(2-3), 571–607 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hautus, M.L.J.: Controllability and observability conditions of linear autonomous systems. Indag. Math. 31, 443–448 (1969)

    MathSciNet  Google Scholar 

  16. Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)

    MATH  Google Scholar 

  17. Morozan, T.: Parametrized Riccati equations for controlled linear differential systems with jump Markov perturbations. Stochastic Anal. Appl. 16(4), 661–682 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ostrowski, A.M.: Über die Determinanten mit überwiegender Hauptdiagonale. Comm. Math. Helv. 10, 69–96 (1937)

    Article  MathSciNet  Google Scholar 

  19. Schneider, H.: Positive operators and an inertia theorem. Numer. Math. 7, 11–17 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sontag, E.D.: Mathematical Control Theory, Deterministic Finite Dimensional Systems, 2nd edn. Springer, New York (1998)

    MATH  Google Scholar 

  21. Tessitore, G.: Some remarks on the detectability condition for stochastic systems. In: Da Prato, G. (ed.) Partial differential equation methods in control and shape analysis. Lect. Notes Pure Appl. Math., vol. 188, pp. 309–319. Marcel Dekker, New York (1997)

    Google Scholar 

  22. Ugrinovskii, V.: Randomized algorithms for robust stability and guaranteed cost control of stochastic jump parameter systems with uncertain switching policies. J. Optim. Th. & Appl. 124(1), 227–245 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Van Willigenburg, L., De Koning, W.: Linear systems theory revisited. Automatica 44, 1686–1696 (2008)

    Article  MATH  Google Scholar 

  24. Zhang, W., Chen, B.-S.: On stabilizability and exact observability of stochastic systems with their applications. Automatica 40, 87–94 (2004)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, TU Kaiserslautern., D-67663, Kaiserslautern, Germany

    Tobias Damm & Cristina Ethington

Authors
  1. Tobias Damm
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  2. Cristina Ethington
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Editor information

Editors and Affiliations

  1. Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camí de Vera s/n, 46022, Valencia, Spain

    Rafael Bru  & Sergio Romero-Vivó  & 

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Damm, T., Ethington, C. (2009). Detectability, Observability, and Asymptotic Reconstructability of Positive Systems. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-02894-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02893-9

  • Online ISBN: 978-3-642-02894-6

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