Zhonghuai Wu, Jianying Shao, Mingquan Yang, Wei Gao (2011)
Annales Polonici Mathematici
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We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].
Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan (2015)
Czechoslovak Mathematical Journal
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We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones....
Mathew Omonigho Omeike (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper a number of known results on the stability and boundedness of solutions of some scalar third-order nonlinear delay differential equations are extended to some vector third-order nonlinear delay differential equations.
Pham Huu Anh Ngoc, Le Trung Hieu (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.
Youssef Raffoul, Habib Rai (2016)
Nonautonomous Dynamical Systems
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In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]
Michael I. Gil' (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady...
Moussadek Remili, Lynda D. Oudjedi (2016)
Archivum Mathematicum
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In this paper, we establish some new sufficient conditions which guarantee the stability and boundedness of solutions of certain nonlinear and non autonomous differential equations of third order with delay. By defining appropriate Lyapunov function, we obtain some new results on the subject. By this work, we extend and improve some stability and boundedness results in the literature.
Wang, Wansheng (2010)
Journal of Inequalities and Applications [electronic only]
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Larbi Fatmi, Moussadek Remili (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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This paper investigates the stability of the zero solution and uniformly boundedness and uniformly ultimately boundedness of all solutions of a certain vector differential equation of the third order with delay. Using the Lyapunov–Krasovskiĭ functional approach, we obtain a new result on the topic and give an example for the related illustrations.
Kostas Hrissagis, Olga I. Kosmidou (1998)
Kybernetika
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The robust stabilization of uncertain systems with delays in the manipulated variables is considered in this paper. Sufficient conditions are derived that guarantee closed-loop stability under state-feedback control in the presence of nonlinear and/or time-varying perturbations. The stability conditions are given in terms of scalar inequalities and do not require the solution of Lyapunov or Riccati equations. Instead, induced norms and matrix measures are used to yield some easy to test...