Abstract
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.
Highlights
Differential systems, or more generally functional differential systems, have been studied rather extensively for at least 200 years and are used as models to describe transportation systems, communication networks, teleportation systems, physical systems and biological systems, and so forth
Caputo fractional differential systems have been studied in many types of stability such as uniform stability [9], Mittag-Leffler stability [10,11,12,13], Ulam stability [14], finite time stability [15,16] and asymptotic stability [17,18]
We introduce a differential and fractional differential neutral system with constant delays and nonlinear perturbation q t0 Dt [ x ( t ) + Cx ( t − τ )]
Summary
Differential systems, or more generally functional differential systems, have been studied rather extensively for at least 200 years and are used as models to describe transportation systems, communication networks, teleportation systems, physical systems and biological systems, and so forth. During the last 10 years fractional-order systems have been widely investigated as they have the qualification to explain various phenomena more precisely in many fields, for example, biological models, material science, finance, cardiac tissues, quantum mechanics, viscoelastic systems, medicine and fluid mechanics [1,2,3,4,5,6,7,8]. Caputo fractional differential systems have been studied in many types of stability such as uniform stability [9], Mittag-Leffler stability [10,11,12,13], Ulam stability [14], finite time stability [15,16] and asymptotic stability [17,18].
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