Skip to main content

L2-disturbance attenuation for linear systems with bounded controls: An ARE-based approach

  • Chapter
  • First Online:
Control of Uncertain Systems with Bounded Inputs

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 227))

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Alvarez-Ramírez, R. Suárez and J. Alvarez, Semi-global stabilization of multi-input linear systems with saturated linear state feedback, Syst. & Contr. Lett., 23 (1994) 247–254.

    Google Scholar 

  2. P. Bolzern, P. Colaneri and G. de Nicolao, Finite escape-times and convergence properties of the H -differential Riccati equation. 13th Triennial World Congress IFAC San Francisco CA, USA (1996) 161–166.

    Google Scholar 

  3. C. Burgat, S. Tarbouriech and M. Klai, Continuous-time saturated state feedback regulators: theory and design, Int. J. Syst, Sci., 25(1994) 315–336.

    Google Scholar 

  4. Y. Chitour, W. Liu and E. Sontag, On the continuity and incremental-gain properties of certain saturated linear feedback loops, Int. J. Robust Nonl. Contr., 5(1995) 413–440.

    Google Scholar 

  5. J. Doyle, Analysis of Feedback Systems with Structured Uncertainties, IEE Proceedings, Part D, 129(1982) 242–250.

    Google Scholar 

  6. J.C. Doyle, K. Glover, P.P. Khargonekar and B. Francis, State-space solutions to the standard H 2 and H control problems, IEEE Trans. Automat. Contr., 34(1989) 831–849.

    Article  Google Scholar 

  7. A.T. Fuller, In-the-large stability of relay and saturating control systems with linear controllers, Int. J. Control, 10(1969) 457–480.

    Google Scholar 

  8. V.M. Gavrilyako, V.I. Korobov and G.M. Sklyar, Designing a bounded control of dynamic systems in entire space with the aid of a controllability function, Automation and Remote Contr., 11(1986) 1484–1490.

    Google Scholar 

  9. J.W. Helton and W. Zhan, Piecewise Riccati equations and the Bounded Real Lemma, Proc. 32th. IEEE Conference on Decision and Contr., (1993) 196–201.

    Google Scholar 

  10. M. Hirsh & S. Smale, Differential equations, dynamical systems and linear algebra. Academic Press (1974).

    Google Scholar 

  11. A. Isidori, Control Systems (in Italian), Roma: SIDEREA (1993).

    Google Scholar 

  12. V.A. Komarov, Design of constrained controls for nonautonomous linear systems, Automation and Remote Contr., 10(1985) 1280–1286.

    Google Scholar 

  13. V.I. Korobov, A general approach to the solution of the bounded control synthesis problem in a controllability problem, Math. USSR Sbornik, 37(1985) 535–539.

    Article  Google Scholar 

  14. S. Lefschetz, Stability of Nonlinear Control Systems. New York: Academic Press, (1965).

    Google Scholar 

  15. Z. Lin and A. Saberi, Semi-global exponential stabilization of linear systems subject to „input saturation” via linear feedbacks, Syst. & Contr. Letters, 21(1993) 225–239.

    Google Scholar 

  16. Z. Lin, A. Saberi and A.R. Teel, Simultaneous L p -stabilization and internal stabilization of linear systems subject to input saturation: State feedback case, Syst. & Contr. Letters, 25 (1995) 219–226.

    Google Scholar 

  17. I.R. Petersen, Disturbance attenuation and H optimization: A design method based on the algebraic Riccati equation, IEEE Trans. Automat. Contr., 32(1987) 427–429.

    Article  Google Scholar 

  18. M.A. Poubelle, R.R. Bitmead and M.R. Gevers, Fake algebraic Riccati techniques and stability, IEEE Trans. Autom. Contr., 33, 4, (1988) 379–381.

    Article  Google Scholar 

  19. B.G. Romanchuk, On the computations of the induced L 2 norm of single input linear systems with saturation, Proc. 33th. IEEE Conference on Decision and Contr., (1994) 1427–1432.

    Google Scholar 

  20. H. Rotstein and A. Sideris, H Optimization with Time-Domain Constraints, IEEE Trans. Autom. Contr., 39, 4, (1994) 762–779.

    Article  Google Scholar 

  21. E.M. Stein, G. Weiss, Fourier Analysis in Euclidean Space, Princeton Univ. Press, Princeton NJ (1971).

    Google Scholar 

  22. S. Skogestad, M. Morari and J. Doyle, Robust Control of Ill-Conditioned Plants: High-Purity Distillation, IEEE Trans. Autom. Contr., 33, 12, (1988) 1092–1105.

    Google Scholar 

  23. A. Sideris and H. Rotstein, Single Input-Single Output H Control with Time Domain Constraints, Automatica, 29, 4, (1993) 969–984.

    Article  Google Scholar 

  24. E.D. Sontag and H.J. Sussmann, Nonlinear output feedback design for linear systems with saturating controls, Proc. 29th. IEEE Conference on Decision and Contr., (1990) 3414–3416.

    Google Scholar 

  25. R. Suárez, J. Alvarez, and J. Alvarez, Regions of Attraction of Closed Loop Linear Systems with Saturated Linear Feedback Journal of Math. Syst., Est., Contr., (To appear).

    Google Scholar 

  26. R. Suárez, J. Solis-Daun, and J. Alvarez, Stabilization of linear control systems by means of bounded continuous nonlinear feedback control, Syst. & Contr. Letters, 23 (1994) 403–410.

    Google Scholar 

  27. R. Suárez, J. Alvarez-Ramírez and J. Solis-Daun, Linear systems with bounded inputs: Global stabilization with eigenvalue placement, Int. J. Robust Nonl. Contr., (to appear).

    Google Scholar 

  28. H.J. Sussmann, E. Sontag and Y. Yang, A general result on stabilization of linear systems using bounded control, IEEE Trans. Autom. Contr., 39 (1994) 2411–2424.

    Article  Google Scholar 

  29. M. Sznaier, “Mixed l 1/H Controllers for SISO Discrete-Time Systems,” Syst. & Contr. Letters, 23 (1994) 487–492.

    Google Scholar 

  30. M. Sznaier, “A Mixed l /H Optimization Approach to Robust Controller Design,” SIAM Journal Opt. Contr., to appear (1995).

    Google Scholar 

  31. M. Sznaier and F. Blanchini, “Robust Control of Constrained Systems via Convex Optimization,” International Journal of Robust and Nonlinear Control, to appear (1995).

    Google Scholar 

  32. A.R. Teel, Global stabilization and restricted tracking for multiple integrators with bounded controls, Syst. & Contr. Letters, 18(1992) 165–171.

    Google Scholar 

  33. A.R. Teel, Semiglobal stabilizability of linear null controllable systems with input nonlinearities, IEEE Trans. Autom. Contr., 40, 1, (1995) 96–100.

    Article  Google Scholar 

  34. M. Vidyasagar, Optimal Rejection of Persistent Bounded Disturbances, IEEE Trans. Autom. Contr., 31, 6, (1986) 527–535.

    Article  Google Scholar 

  35. G. Zames, Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms and Approximate Inverses, IEEE Trans. Autom. Contr. 26, 4, (1981) 301–320.

    Article  Google Scholar 

  36. K. Zhou, J. Doyle and K. Glover, Robust and Optimal Control, Prentice-Hall 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Sophie Tarbouriech Germain Garcia

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag London Limited

About this chapter

Cite this chapter

Suárez, R., Alvarez-Ramírez, J., Sznaier, M., Ibarra-Valdez, C. (1997). L2-disturbance attenuation for linear systems with bounded controls: An ARE-based approach. In: Tarbouriech, S., Garcia, G. (eds) Control of Uncertain Systems with Bounded Inputs. Lecture Notes in Control and Information Sciences, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032162

Download citation

  • DOI: https://doi.org/10.1007/BFb0032162

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76183-9

  • Online ISBN: 978-3-540-40936-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics