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Performance Robustness Analysis via Root Clustering (Robust D-Stability)

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Robust Control of Uncertain Dynamic Systems
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Abstract

In this chapter, we address the issue of performance robustness, in contrast to stability robustness discussed in the previous chapter. We assume that “performance” of the control system is characterized by speed of response which in turn is a function of the location of the eigenvalues of the closed-loop system. Thus, we treat the performance robustness problem as robust D-stability problem where the D-stability region is a subregion in the complex plane.

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References

  1. S Gutman and E.I Jury. A general theory for matrix root clustering in subregions of the complex plane. IEEE Trans on Automatic Control, 26:403, 1981.

    Google Scholar 

  2. B. R Barmish. A generalization of kharitonov’s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations. IEEE Trans Auto. Control, AC-34:157–165, 1989.

    Google Scholar 

  3. M Fu and B. R. Barmish. Polytopes of polynomials with zeros in a prescribed set. IEEE Trans On Autom. Control, 34:544, 1989.

    Google Scholar 

  4. C.B Soh. On extending the hypersphere method to handle dominant pole assignment. IEEE Trans On Autom. Control, 34:543, 1989.

    Google Scholar 

  5. H Kokame and T Mori. A root distribution criterion for interval polynomials. IEEE Trans on Automatic Control, 36:362, 1991.

    Google Scholar 

  6. J Ackermann, D Kaesbauer, and R Muench. Robust gamma stability analysis in plant parameter space. Automatica, 27:75, 1991.

    Google Scholar 

  7. A. Vicino. Robustness of pole location in perturbed systems. Autmoatica, 25:109, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  8. E Zeheb. Necessary and sufficient conditions for root clustering of a polytope of polynomials in a simply connected domain. IEEE Trans Auto. Control, 34:986, 1989.

    Google Scholar 

  9. Y. T Juang, Z.C Hong, and Y.T Wang. Robustness of pole-assignment in a specified region. IEEE Trans On Autom. Control, 34:758, 1989.

    Google Scholar 

  10. Y. T Juang. Robust stability and robust pole assignment of linear systems with structured uncertainty. IEEE Trans on Automatic Control, 36:635, 1991.

    Google Scholar 

  11. K.M. Sobel and W.Yu. Flight control application of eigenstructure assignment with optimization of robustness to structure state space uncertainty,. 28th IEEE Conf. Decision and Control, Tampa,FL, pages 1705–1707, 1989.

    Google Scholar 

  12. L. H. Keel, K. B. Lim, and J. N. Juang. Robust eigenvalue assignment with maximum tolerance to system uncertainties. J. Guid. Cont. Dyn., pages 615–620, 1991.

    Google Scholar 

  13. A.Tesi and A. Vicino. Robust stability of state space models with structured uncertainties. IEEE Trans on Automatic Control, 35:191–195, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  14. A.A Abdul-Wahab. Lyapunov bounds for root clustering in the presence of system uncertainty. International Journal of Systems Science, 21:2603, 1990.

    Google Scholar 

  15. A.A Abdul-Wahab. Perturbation bounds for root clustering of linear continuous time systems. International Journal of Systems Science, 22:921, 1991.

    Google Scholar 

  16. R. K Yedavalli. Counterexample to a recent result on perturbation bounds for root clustering by a.a. abdul-wahab. International Journal of Systems Science, 23:661, 1992.

    Google Scholar 

  17. R.K.Yedavalli. Robust root clustering for linear uncertain systems using generalized lyapunov theory. Automatica, 29:237–240, January 1993.

    Article  MathSciNet  MATH  Google Scholar 

  18. R. K Yedavalli. A non-conservative kronecker based theory for robust root clustering of linear state space models with real norm bounded uncertainty. In M Mansour, S Balemi, and Truol, editors, Robustness of Dynamic Systems with Parameter Uncertainties, pages 155–164. Birkhauser, 1992.

    Google Scholar 

  19. R. K Yedavalli. Extension of gutman and jury’s theory of root clustering to perturbed matrices. In M Jamshidi, M Mansour, B.D.O Anderson, and N.K Bose, editors, Fundamentals of Discrete Time Systems (A Tribute to Prof. E.I.Jury), pages 457–464. TSI Press, 1993.

    Google Scholar 

  20. S.R Kolla, R. K Yedavalli, and J.B Farison. Robust stability bounds of linear discrete time systems. Int. J of Control, 50:151, 1989.

    Google Scholar 

  21. L.H. Keel, S.P.Bhattacharya, and J.W. Howze. Robust control with structured perturbations. AC-33(68–78), 1988.

    Google Scholar 

  22. K. Zhou and P. Khargonekar. Stability robustness bounds for linear state space models with structured uncertainty. IEEE Transactions on Automatic Control, AC-32:621–623, July 1987.

    Article  MathSciNet  Google Scholar 

  23. L.Qiu and E.J. Davison. The stability robustness determination of state space models with real unstructured perturbations. Mathematics of Control, Signals and Systems, 2:247–267, 1991.

    Google Scholar 

  24. L Qiu and E. J. Davison. A new method for the stability robustness determination of state space models with real perturbations. Proceedings of IEEE Conference on Decision and Control, page 538, 1988.

    Google Scholar 

  25. K.S Yeung. Linear discrete time system stability under parameter variations. Int. J of Control, 40:855–862, 1984.

    Google Scholar 

  26. T Mori and H Kokame. A necessary and sufficient condition for stability of linear discrete systems with parameter variation. Journal of Franklin Institute, 321:135, 1986.

    Google Scholar 

  27. C.B Soh, C.S Berger, and K.P Dabke. On stability of polynomials with perturbed coefficients. IEEE Trans on Automatic Control, 30(10):1032–1033, 1985.

    Google Scholar 

  28. J Cieslik. On the possibility of the extension of kharitonov’s stability test for interval polynomials to the discrete-time case. IEEE Trans Auto. Control, 32:237, March 1987.

    Google Scholar 

  29. C. V Hollot and A Bartlett. Some discrete-time counterparts to kharitonov’s stability criterion for uncertain systems. IEEE Trans On Autom. Control, 31:355, April 1986.

    Google Scholar 

  30. T Mori and H Kokame. Convergence property of interval matrices and interval polynomials. Int. J of Control, 45(2):481, 1987.

    Google Scholar 

  31. R.K.Yedavalli and Y. Liu. H-infinity control with regional stability constraints. Automatica, 31:611–615, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  32. Y. Liu and R.K.Yedavalli. Linear quadratic control with stability degree constraints. Systems and Control Letters, 21:181–187, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  33. V. Leite and P. Peres. An improved lmi condition for robust d-stability of uncertain polytopic systems. IEEE Transactions on Automatic Control, 48(3):500–504, 2003.

    Article  MathSciNet  Google Scholar 

  34. W. Mao and J. Chu. Robust d-stability and d-stabilization of dynamic interval systems. International Journal of Control, Automation, and Systems, 5(5):594–600, Oct 2007.

    Google Scholar 

  35. F Amato, M Mattei, and A Pironti. A note on quadratic stability of uncertain linear discrete time systems. IEEE Trans on Automatic Control, 43:227–229, 1998.

    Google Scholar 

  36. M Chilali, P Gahinet, and P Apkarian. Robust pole placement in lmi regions. IEEE Trans on Automatic Control, 44:2257–2270, 1999.

    Google Scholar 

  37. C.R. Ashokkumar and R.K.Yedavalli. Eigenstructure perturbation analysis in disjointed domains for uncertain systems. International Journal of Control, 67:887–899, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  38. C.R Ashokkumar and R. K Yedavalli. Time response bounds for linear uncertain systems with structured uncertainty. International Journal of Systems Science, 31(2):177–188, 2000.

    Google Scholar 

  39. K Zhou, J.C Doyle, and K. Glover. Robust and Optimal control. Prentice Hall, Upper Saddle River, NJ, 1996.

    Google Scholar 

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Yedavalli, R.K. (2014). Performance Robustness Analysis via Root Clustering (Robust D-Stability). In: Robust Control of Uncertain Dynamic Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9132-3_3

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  • DOI: https://doi.org/10.1007/978-1-4614-9132-3_3

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  • Publisher Name: Springer, New York, NY

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