Global and Local Weighted Homogeneity for Time-Delay Systems
Abstract
The notion of weighted homogeneity is extended to the time-delay systems. It is shown that the stability/instability of homogeneous functional systems on a sphere implies the global stability/instability of the system. The notion of local homogeneity is introduced, a relation between stability/instability of the locally approximating dynamics and the original time-delay system is established using Lyapunov-Razumikhin approach. An implication between homogeneity and input-to-state stability is investigated. Examples of application of the proposed theory are given.
Domains
Automatic
Origin : Files produced by the author(s)
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