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New qualitative methods for stability of delay systems. (English) Zbl 1265.93191
Summary: A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known qualitative behavior. It leads to criteria for stability of general difference and delay differential equations.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D30 Lyapunov and storage functions
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