Displaying similar documents to “On the “freezing” method for nonlinear nonautonomous systems with delay.”

Stability and sliding modes for a class of nonlinear time delay systems

Vladimir B. Răsvan (2011)

Mathematica Bohemica

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The following time delay system x ˙ = A x ( t ) + 1 r b q i * x ( t - τ i ) - b ϕ ( c * x ( t ) ) is considered, where ϕ : may have discontinuities, in particular at the origin. The solution is defined using the “redefined nonlinearity” concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given.

Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay

Moussadek Remili, Lynda Damerdji Oudjedi (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this article, we shall establish sufficient conditions for the asymptotic stability and boundedness of solutions of a certain third order nonlinear non-autonomous delay differential equation, by using a Lyapunov function as basic tool. In doing so we extend some existing results. Examples are given to illustrate our results.