New delay-range-dependent exponential stability criteria for certain neutral differential equations with interval discrete and distributed time-varying delays

Abstract

In this research, we investigate the problem of delay-dependent exponential stability analysis for certain neutral differential equations with discrete and distributed time-varying delays. The time-varying delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available. The restrictions on the derivative of interval time-varying delays are needed. Based on a class of novel augmented Lyapunov-Krasovskii functionals, a model transformation, the decomposition technique of constant coefficients, the Leibniz-Newton formula, and utilization of a zero equation, new delay-range-dependent exponential stability criteria are derived in terms of the linear matrix inequality (LMI) for the equations considered. Numerical examples suggest for the results given to illustrate the effectiveness and improvement over some existing methods.

A New Approach for Exponential Stability Criteria of New Certain Nonlinear Neutral Differential Equations with Mixed Time-Varying Delays

“…Remark 1. It should be pointed out that the problem of the delay differential equation with distributed delay function of tanh x(s) is more general than [16], where the delay is not considered. Generally applicable nonlinear system contain with mixed time-varying delays, for instance the population dynamics and predator-prey model that were studied in [17][18][19].…”

“…In a practical system, the distributed delay is often useful in modeling processes that are (i) described by flow rates (aggregates) of entities that move at different rates through the given irreversible process (ii). Recently, a certain neutral differential equation with distributed and discrete time-varying delays was considered in [16] as follows:…”

“…The exponential stability criteria are in the form of linear matrix inequalities (LMIs). Second, note that most of the existing NDE results [1,9,[14][15][16] cannot be applied to the situation when there are two distributed time-varying delays. Finally, a comparison of the maximum delay bounds obtained by our proposed methods with those in many existing literature works [1,9,14,15] is conducted, which supports that the exponential stability criteria provided in this paper can enhance the feasible region effectively and significantly.…”

“…14,14) = −β 6 e −2ατ 2 , Φ(15,15) = −β 7 e −2ασ 2 , Φ(16,16) = −η 3 e −2ατ 1 , Φ (17,17) = −η 4 e −2ασ 1 , Φ (18,18) = −η 5 e −2ατ1 , Φ (19,19) = −β 10 e −2ασ 2 , Φ (20,20) = −η 6 σ 1 e −2ασ 1 , Φ (21,21) = −η 7 e −2αh 2 , Φ (22,22) = −η 8 e −2αl 2 , Φ (23,23) = −η 9 e −2αh 1 , Φ (24,24) = −η 10 e −2αl 1 , other terms are zero.…”

New Exponential Stability Criteria for Certain Neutral Integro-Differential Equations

“…Therefore, qualitative behaviors of solutions NIDEs, stability, boundedness, convergence, instability, integrability, globally existence of solutions, etc., have been extensively investigated in the literature by this time. For a comprehensive treatment of these qualitative properties of solutions of NIDEs and some applications, we refer the readers to the papers or books of Hale et al (1993), Boyd et al (1994), Agarwal and Grace (2000), El-Morshedy and Gopalsamy (2000), Fridman (2001), Fridman (2002), Gu et al (2003), Park (2004), Kwon and Park (2006), Sun and Wang (2006), Kwon and Park (2008), Park and Kwon (2008), Deng et al (2009), Liao et al (2009), Li New Exponential Stability Criteria for Certain Neutral Integro-Differential Equations 120 (2009), Nam and Phat (2009), Rojsiraphisal and Niamsup (2010), Chen et al (2011), Chen and Huabin (2012), Tunç and Altun (2012), Tunç (2013), Pinjai and Mukdasai (2013), Li and Fu (2013), Keadnarmol et al (2014), Chatbupapan et al (2016), Gözen and Tunç (2017a and b), Tunç and Mohammed (2017), Gözen and Tunç (2018), Tunç and Tunç (2018), Hristova and Tunç (2019), Slyn'ko and Tunç (2019) and the references can be found in these sources. In a particular case, we should mention the following related paper on the qualitative behaviors of the solutions of NIDEs .…”