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On delay-dependent robust stability under model transformation of some neutral systems

Salvador A. Rodríguez, Luc Dugard, Jean-Michel Dion, Jesús de León (2009)

Kybernetika

This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability...

On delay-dependent stability for neutral delay-differential systems

Qing-Long Han (2001)

International Journal of Applied Mathematics and Computer Science

This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.

On oscillation of solutions of forced nonlinear neutral differential equations of higher order II

N. Parhi, R. N. Rath (2003)

Annales Polonici Mathematici

Sufficient conditions are obtained so that every solution of [ y ( t ) - p ( t ) y ( t - τ ) ] ( n ) + Q ( t ) G ( y ( t - σ ) ) = f ( t ) where n ≥ 2, p,f ∈ C([0,∞),ℝ), Q ∈ C([0,∞),[0,∞)), G ∈ C(ℝ,ℝ), τ > 0 and σ ≥ 0, oscillates or tends to zero as t . Various ranges of p(t) are considered. In order to accommodate sublinear cases, it is assumed that 0 Q ( t ) d t = . Through examples it is shown that if the condition on Q is weakened, then there are sublinear equations whose solutions tend to ±∞ as t → ∞.

On oscillation of solutions of forced nonlinear neutral differential equations of higher order

N. Parhi, Radhanath N. Rath (2003)

Czechoslovak Mathematical Journal

In this paper, necessary and sufficient conditions are obtained for every bounded solution of [ y ( t ) - p ( t ) y ( t - τ ) ] ( n ) + Q ( t ) G y ( t - σ ) = f ( t ) , t 0 , ( * ) to oscillate or tend to zero as t for different ranges of p ( t ) . It is shown, under some stronger conditions, that every solution of ( * ) oscillates or tends to zero as t . Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.

On robust stability of neutral systems

Silviu-Iulian Niculescu (2001)

Kybernetika

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.

On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

Mikhail Kamenskii, Valeri Obukhovskii, Jen-Chih Yao (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.

On stability of linear neutral differential equations with variable delays

Leonid Berezansky, Elena Braverman (2019)

Czechoslovak Mathematical Journal

We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays x ˙ ( t ) - a ( t ) x ˙ ( g ( t ) ) + b ( t ) x ( h ( t ) ) = 0 , where | a ( t ) | < 1 , b ( t ) 0 , h ( t ) t , g ( t ) t , and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

On the asymptotic behavior of a class of third order nonlinear neutral differential equations

Blanka Baculíková, Jozef Džurina (2010)

Open Mathematics

The objective of this paper is to study asymptotic properties of the third-order neutral differential equation a t x t + p t x σ t ' ' γ ' + q t f x τ t = 0 , t t 0 . E . We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.

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