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Robust Analysis of Feedback Systems with Parametric and Dynamic Structured Uncertainty


Sánchez Peña, Ricardo Salvador (1989) Robust Analysis of Feedback Systems with Parametric and Dynamic Structured Uncertainty. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MM2J-E556.


This thesis presents the first general program implementation of the algorithm by deGaston and its generalization by Sideris and deGaston to compute the Multivariable stability margin or Structured singular value of a feedback system under real (independent or related) parametric uncertainty. An improved implementation of the algorithm mentioned above is also considered, which simplifies significantly the code and increases the computational speed. The latter also allows a simple and fast analysis by just checking the extreme values of the set of parameters, with a high probability of achieving the actual stability margin; this being supported by an intense statistical analysis performed at the end of this thesis.

A great deal of work has recently been done related to this class of uncertain systems initiated by the well known theorem of Kharitonov. A connection is made in Chapter 4 between these procedures and the above ones in terms of generality of the class of uncertain polynomials considered. A theorem characterizing the set of polynomials whose robust stability can be determined by a finite number of tests is addressed. Sufficient conditions to determine when the latter conditions apply are also given, which in some cases can considerably simplify the analysis. In particular cases, polynomials with related uncertain parameters can be treated in the same way as independent parameters as shown in two examples.

The main part of this thesis is concerned with the analysis of more general type of uncertainties. In particular, the analysis of robust stability for the case when unstructured dynamic uncertainty is combined with real parametric uncertainty is treated in Chapter 5. This can also be applied in the analysis of robust performance for plants with parametric uncertainty. Chapter 6 generalizes the latter to the most general case in which structured dynamic and real parametric uncertainty appear simultaneously in the plant. A computational scheme is given in both cases which uses the algorithm mentioned in the first part and is applied to several examples.

At the end, an example of the robust analysis of an experimental aircraft demonstrates how a practical situation can be handled by this procedure.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:robustness analysis, dynamic, parametric and mixed uncertainty
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Sideris, Athanasios (advisor)
  • Martel, Hardy Cross (co-advisor)
Thesis Committee:
  • Sideris, Athanasios (chair)
  • Beck, James L.
  • Doyle, John Comstock
  • Lorentz, G. G.
  • Lorenz, Jens
  • Martel, Hardy Cross
  • Morari, Manfred
  • Vaidyanathan, P. P.
Defense Date:3 June 1988
Funding AgencyGrant Number
Organization of American StatesUNSPECIFIED
Comisión Nacional de Investigacioes EspacialesUNSPECIFIED
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)UNSPECIFIED
Record Number:CaltechETD:etd-02012005-084251
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:425
Deposited By: Imported from ETD-db
Deposited On:01 Feb 2005
Last Modified:21 Oct 2021 00:00

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