2005/11/15 by Eugenii Shustin, Eugeniĭ Shustin, Emilia Fridman +2
Engineering · Mathematics · #26D10 #93B36 #93D05 #Control and Stability of Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #math.FA #math.OC #msc:26D10 #msc:93B36 #msc:93D05
paper · pdf · doi:10.48550/arxiv.math/0511375
6 pages, 4 figures, presented at ROCOND-06, some defects corrected
openalex publication_date 2005/11/15 · arxiv created 2006/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the L2-norm of a certain integral operator. There exists a bound on this operator in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving an operator bound which is an increasing and continuous function of the delay derivative upper bound d ≥ 1. For d→ ∞ the new bound corresponds to the second case and improves the existing bound. As a result, improved frequency-domain and time-domain stability criteria are erived for systems with the delay derivative greater than 1.