On delay-dependent stability under model transformations of some neutral linear systems

By Silviu-Iulian Niculescu. 2001

146 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b44af801487576e45f598c5f588256128f46df7c

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Delay‐dependent stability and stabilization of neutral time‐delay systems (2009, methodology): “Using the Lyapunov–Razumikhin functional approach or the Lyapunov– Krasovskii functional approach, delay-independent [3, 4] and delay-dependent stability criteria [5–11] have been proposed.”
Overview of recent advances in stability of linear systems with time‐varying delays (2019, methodology): “There are a number of model transformation approaches proposed in the literature, namely, ‘first-order transformation’ [32], ‘parameterised first-order transformation’ [33], ‘second-order transformation’ [34], ‘neutral transformation’ [35] and ‘descriptor model transformation’ [36, 37].”
A survey of linear matrix inequality techniques in stability analysis of delay systems (2008, methodology): “…Hui and Hu 1997; Dugard and Verriest 1998; Su and Chu 1999; Hmamed 2000; Shi, Agarwal, Boukas, and Shue 2000; Wang and Unbehauen 2000; Liu 2001; Niculescu 2001a; Boukas and Liu 2002; Boukas, Liu, and Shi 2002; Fridman and Shaked 2002a; Xu, Lam, and Yang 2002; Xu, Van Dooren, Stefan, and Lam…”
Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology (2011, unknown): “Also, note that α1‖D(x̃(n−1)t)‖ ≤ V(x̃(n−1)t)≤α2‖x̃(n−1)t‖c [24], where D(x̃(n−1)t)= x̃n−1(t)− ∫ 0 −τ1 x̃n−1(t + θ) dθ+Ã ∫ 0 −τ1−τ2 x̃n−1(t + θ) dθ, ‖x̃(n−1)t‖c = supθ∈[−τ1−τ2,0] ‖x̃(n−1)(t + θ)‖, α1 = λmin(Pfc), and α2 = λmax(Pfc) + τ1λmax(Sfc) + (τ1 + τ2)λmax(Hfc).”
Stability analysis for neutral systems with mixed delays (2007, background): “Other papers have presented criteria that depend only on the size of the discrete delays, and not on the size of the neutral delays: see, for example, [5,10,15,17].”
Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time‐delay systems (2006, background): “In order to obtain a reasonable actual delay bound of (71) analytically for this particular selection of uncertainty matrix, one needs to solve the characteristic equation DðsÞ 1⁄4 jsI % A % Ade stj for s 1⁄4 jo to get a non-zero pole on the imaginary axis [15].”