Robust stability with structured real parameter perturbations

This paper considers the problem of robust stabilization of a linear time-invariant system subject to variations of a real parameter vector. For a given controller the radius of the largest stability hypersphere in this parameter space is calculated. This radius is a measure of the stability margin...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1987-06, Vol.32 (6), p.495-506
Main Authors: Biernacki, R., Humor Hwang, Bhattacharyya, S.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Applied sciences
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Exact sciences and technology
Feedback control
Iterative algorithms
Polynomials
Robust control
Robust stability
Robustness
Transfer functions
Vectors
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Summary:This paper considers the problem of robust stabilization of a linear time-invariant system subject to variations of a real parameter vector. For a given controller the radius of the largest stability hypersphere in this parameter space is calculated. This radius is a measure of the stability margin of the closed-loop system. The results developed are applicable to all systems where the closed-loop characteristic polynomial coefficients are linear functions of the parameters of interest. In particular, this always occurs for single-input (multioutput) or single-output (multiinput) systems where the transfer function coefficients are linear or affine functions of the parameters. Many problems with transfer function coefficients which are nonlinear functions of physical parameters can be cast into this mathematical framework by suitable weighting and redefinition of functions of physical parameters as new parameters. The largest stability hyperellipsoid for the case of weighted perturbations and a stability polytope in parameter space are also determined. Based on these calculations a design procedure is proposed to robustify a given stabilizing controller. This algorithm iteratively enlarges the stability hypersphere or hyperellipsoid in parameter space and can be used to design a controller Io stabilize a plant subject to given ranges of parameter excursions. These results are illustrated by an example.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.1987.1104648