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The graph metric for unstable plants and robustness estimates for feedback stability. (English) Zbl 0536.93042
The main aim of this paper is to study the robustness of feedback stability problems using a ”graph metric” defined as a notion of a distance between unstable multivariable plants. This concept induces a ”graph topology” on the set of unstable plants where a perturbation of the plant consists of perturbations of the ”numerator” and ”denominator” of the plant transfer matrix, when it is expressed as a ratio of stable transfer matrices. The author shows that it is the case of the weakest topology in which feedback stability is robust. The graph metric is then used to derive some estimates for the robustness of feedback stability. The preceding results are used to study the design of controllers for unstable singularly perturbed systems. Then the extension of the results obtained in the paper to the case of distributed systems is discussed. Also the relationship to the ”gap metric” introduced in some earlier work is considered in the last part of the paper, which will probably be of most interest to theorists working in control theory.
Reviewer: J.Wicher

93D15 Stabilization of systems by feedback
93B35 Sensitivity (robustness)
93C35 Multivariable systems, multidimensional control systems
93B05 Controllability
93C10 Nonlinear systems in control theory
34D15 Singular perturbations of ordinary differential equations
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
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