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Sets and Constraints in the Analysis of Uncertain Systems


Paganini-Herrera, Fernando (1996) Sets and Constraints in the Analysis of Uncertain Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3X73-5F28.


This thesis is concerned with the analysis of dynamical systems in the presence of model uncertainty. The approach of robust control theory has been to describe uncertainty in terms of a structured set of models, and has proven successful for questions, like stability, which call for a worst-case evaluation over this set. In this respect, a first contribution of this thesis is to provide robust stability tests for the situation of combined time varying, time invariant and parametric uncertainties.

The worst-case setting has not been so attractive for questions of disturbance rejection, since the resulting performance criteria (e.g., H) treat the disturbance as an adversary and ignore important spectral structure, usually better characterized by the theory of stochastic processes. The main contribution of this thesis is to show that the set-based methodology can indeed be extended to the modeling of white noise, by employing standard statistical tests in order to identify a typical set, and performing subsequent analysis in a worst-case setting. Particularly attractive sets are those described by quadratic signal constraints, which have proven to be very powerful for the characterization of unmodeled dynamics. The combination of white noise and unmodeled dynamics constitutes the Robust H2 performance problem, which is rooted in the origins of robust control theory. By extending the scope of the quadratic constraint methodology we obtain a solution to this problem in terms of a convex condition for robustness analysis, which for the first time places it on an equal footing with the H performance measure.

A separate contribution of this thesis is the development of a framework for analysis of uncertain systems in implicit form, in terms of equations rather than input-output maps. This formulation is motivated from first principles modeling, and provides an extension of the standard input-output robustness theory. In particular, we obtain in this way a standard form for robustness analysis problems with constraints, which also provides a common setting for robustness analysis and questions of model validation and system identification.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Awards:Charles and Ellen Wilts Prize, 1996
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Doyle, John Comstock
Thesis Committee:
  • Doyle, John Comstock (chair)
  • Goldsmith, Andrea Jo
  • Marsden, Jerrold E.
  • Murray, Richard M.
  • McEliece, Robert J.
Defense Date:1 December 1995
Record Number:CaltechETD:etd-09172007-080812
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3582
Deposited By: Imported from ETD-db
Deposited On:17 Sep 2007
Last Modified:30 Aug 2022 21:39

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