Skip to main content
Log in

Stability radius of non-smooth pritchard-salamon systems and the algebraic Riccati equation

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The authors discuss the stability radius of the non-smooth Pritchard-Salamon systems under structured perturbations. A formula for the stability radius in terms of the norm of a certain input-output operator is obtained. Furthermore, the relationship between stability radius and the solvability of some type of algebraic Riccati equations is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Clark, Y. Latushkin, S. Montgomery-Smith, and T. Randolph, Stability radius and internal versus external stability in Banach spaces: An evolution semigroup approach, SIAM J. Control Optim., 2000, 38(6): 1757–1793.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Fischer and J. Van Neerven, Robust stability of C 0-semigroups and an application to stability of delay equations, J. Math. Anal. Appl., 1998, 226(1): 82–100.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. Hinrichsen, A. Ilchmann, and A. J. Pritchard, Robustness of stability of time-varying linear systems, J. Diff. Equ., 1989, 82(2): 219–250.

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Hinrichsen and A. J. Pritchard, Stability radius for structured perturbations and the algebraic riccati equation, Systems Control Lett., 1986, 8(2): 105–113.

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Hinrichsen and A. J. Pritchard, Robust stability of linear evolution operators on Banach-spaces, SIAM J. Control Optim., 1994, 32(6): 1503–1541.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. J. Pritchard and S. Townley, Robustness of linear systems, J. Differential Equations, 1989, 77(2): 254–286.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. J. Pritchard and S. Townley, Robustness optimization for uncertain infinite-dimensional systems with unbounded inputs, IMA J. Math. Control Inform., 1991, 8(2): 121–133.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. M. Guo, Q. Zhang, and F. L. Huang, Well-posedness and admissible stabilizability for Pritchard-Salamon systems, Appl. Math. Lett., 2003, 16(1): 65–70.

    Article  MathSciNet  MATH  Google Scholar 

  9. Y. Liu, W. Jiang, and F. Huang, Linear quadratic control and frequency domain inequalities corresponding to the nonsmooth Pritchard-Salamon systems, Sichuan Daxue Xuebao, 2003, 40(5): 816–819.

    MathSciNet  MATH  Google Scholar 

  10. A. J. Pritchard and D. Salamon, The linear quadratic control problem for retarded systems with delays in control and observation, IMA J. Math. Control & Information, 1985, 2(4): 335–362.

    Article  MATH  Google Scholar 

  11. A. J. Pritchard and D. Salamon, The linear quadratic control problem for infinite-dimensional systems with unbounded input and output operators, SIAM J. Control Optim., 1987, 25(1): 121–144.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. F. Curtain, H. Logemann, S. Townley, and H. Zwart, Well-posedness, stabilizability, and admissibility for Pritchard-Salamon systems, J. Math. Systems Estim. Control, 1997, 7(4): 439–476.

    MathSciNet  Google Scholar 

  13. B. Van Keulen, H -Control for Distributed Parameter Systems: A State-Space Approach, Boston, Birkhauser, 1993.

    MATH  Google Scholar 

  14. M. C. Gao and J. C. Hou, Stabilizability and algebraic riccati equations for Pritchard-Salamon systems, Acta Math. Sinica, 2000, 43(4): 577–588.

    MathSciNet  MATH  Google Scholar 

  15. A. J. Sasane and R. F. Curtain, Optimal hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systems, Integral Equations Operator Theory, 2001, 39(1): 98–126.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, New York, Springer-Verlag, 1995.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Weisheng Jiang.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 10626057 and 10571165.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, W., Huang, F. & Zhu, T. Stability radius of non-smooth pritchard-salamon systems and the algebraic Riccati equation. J Syst Sci Complex 22, 220–227 (2009). https://doi.org/10.1007/s11424-009-9158-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-009-9158-6

Key words

Navigation