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Robustness of infinite dimensional systems

By Stuart Townley

Abstract

The results contained within this thesis concern an abstract\ud framework for a robustness analysis of exponential stability of infinite\ud dimensional systems. The abstract analysis relies on the strong\ud relationship between exponential stability and L2-stability which\ud exists for many classes of linear systems.\ud In Chapter 1a "stability radius", for systems governed by semigroups,\ud is developed, for a class of "structured" perturbations of its\ud generator. The abstract theory is illustrated by examples of perturbations\ud of the boundary data for homogeneous boundary value problems and also\ud perturbations arising due to neglected delay terms in differential delay\ud equations.\ud In Chapter 2a related problem of a non standard linear quadratic\ud problem is studied, which leads to a stability analysis for certain nonlinear\ud systems.\ud In Chapter 3 an abstract L2-stability theory is developed and\ud then applied to integrodifferential equations and time-varying systems,\ud to investigate the robustness of exponential stability of such systems

Topics: QA
OAI identifier: oai:wrap.warwick.ac.uk:4374

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Citations

  1. (1986). A Stability radius for infinite dimensional systems", to appear in doi
  2. All optimal Hankel norm approximations for multivariable systems and their Lw-error bounds", doi
  3. (1985). Balanced realisations for infinite dimensional systems", presented at the workshop "Operator Theory and its Applications",
  4. Between controllable and uncontrollable", doi
  5. C business of S. ap44Ly for linear time varying systems", doi
  6. (1976). Convex Analysis and Variational Problems", North Holland Pub.
  7. (1967). Distributed system transfer functions of exponential order", doi
  8. Extending a theorem doi
  9. (1981). Feedback and optimal sensitivity; model reference transformations, multiplicative semi-norms and approximate inverses", doi
  10. Finite dimensional controllers for parabolic distributed systems with unbounded control and observation", doi
  11. (1970). Finite dimensional linear systems",
  12. (1974). Functional analysis", doi
  13. Gain optimisation for distributed plants", doi
  14. (1985). Invariance results for delay and Volterra equations in fractional order Sobolev spaces", doi
  15. (1971). Least squares stationary optimal control and the algebraic Riccati equation", doi
  16. (1957). Linear Operators, Vol . 1", Interscience
  17. (1972). Non-homogeneous boundary value problems, Vol. I", doi
  18. (1985). On linear Volterra equations in Banach spaces", doi
  19. (1980). On robustness of stability of feedback systems", doi
  20. (1980). Quantitative measures of robustness for multivariable''systems".
  21. (1984). Resolvent operators for integral equations in a Banach space", doi
  22. (1984). Stability and stabilizability of infinite dimensional systems",
  23. Stability radii of linear systems" doi
  24. Stability radius for structured perturbations and the algebraic Riccati equation", doi
  25. (1985). The linear quadratic control problem for retarded 'systems with delays in control and observation", doi
  26. (1978). The resolvent kernel of an integrodifferential equation in Hilbert space", doi
  27. (1987). Thesis Universit├Ąt doi

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