An improved stability criterion for a class of neutral differential equations

Abstract

a b s t r a c tThis work gives an improved criterion for asymptotical stability of a class of neutral differential equations. By introducing a new Lyapunov functional, we avoid the use of the stability assumption on the main operators and derive a novel stability criterion given in terms of a LMI, which is less restricted than that given by Park [J.H. Park, Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. Math. Lett. 17 (2004) 1203-1206] and Sun et al. [Y.G. Sun, L. Wang, Note on asymptotic stability of a class of neutral differential equations, Appl. Math. Lett. 19 (2006) 949-953].

Discrete Wirtinger-based inequality and its application

“…In order to obtain less conservative stability conditions, many researchers have pursued along two main research directions: (i) enlarging on the classes of Lyapunov functionals; and (ii) providing tighter estimations of the derivative of the Lyapunov functionals. With regard to the first research direction, many significant results such as the descriptor model transformations [5], delay-decomposition technique [6,7,8], the neutral model transformations [9,10], triple (multiple) integral terms [11,12], Razumikhin technique [13], and delay-dependent matrix technique [14] have been reported. With regard to the second research direction, significant developments such as the free-weighting matrix technique [15], and widely used inequalities such as the Jensen inequality [1], improved Jensen inequalities [16,17], reciprocally convex combination inequality [18], Wirtinger's inequality [19] and Wirtinger-based integral inequality [20,21] have been reported.…”

New delay-partitioning approaches to stability criteria for uncertain neutral systems with time-varying delays

“…(34), (37)- (38), (61)-(62) and by application of the S-procedure [48], if LMI (51) holds, then _ V has a new upper bound given by…”

Numerical stability of one-leg methods for neutral delay differential equations

“…Whereafter, some authors further studied the criterion for asymptotic stability of (1.7) such as Sun and Wang [19], Nam and Phat [16]. But so far in literature we have never seen any stability or contractivity results of numerical methods for the general nonlinear NDDEs (as (2.1) in next section of this paper).…”