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A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems. (English) Zbl 0923.93046
A linear ODE system with constant delay and ‘uncertain’ coefficients is considered. Stability is determined on the basis of a quadratic functional. The technical tools are matrix algebra (as favoured by current textbooks) and the Laplace transform. The discretization schemes are chosen to be partially compatible with these two tools; switchover operations are not mentioned. The objective is to determine the maximal possible delay with a reasonably small effort.
The basic argument relies on a theorem established more than fifty years ago: Asymptotic stability guarantees that deviations from the reference solution will be small in the presence of small constantly acting perturbations (uncorrelated with internal, external and parametric resonances).
The references are limited to the field of control theory.
A theoretical control-engineering paper. No new mathematical methods or ideas.

MSC:
93D09 Robust stability
93B40 Computational methods in systems theory (MSC2010)
93C05 Linear systems in control theory
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