Stability Analysis of Fractional Switched Systems With Stable and Unstable Subsystems

This article addresses stability of fractional switched systems (FSSs) with stable and unstable subsystems. First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. Then, some stability conditions which have less conservation are also provided by utilizing average dwell time (ADT) technique and the property of Mittag-Leffler function. In addition, sufficient conditions on asymptotic stability of delayed FSSs are obtained by virtue of fractional Razumikhin technique. Finally, several examples are given to reveal that the conclusions obtained are valid.

Practical stability for Riemann–Liouville delay fractional differential equations

In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, we define in an appropriate way initial conditions which are deeply connected with the fractional derivative used. We introduce an appropriate generalization of practical stability which we call practical stability in time. Several sufficient conditions for practical stability in time are obtained using Lyapunov functions and the modified Razumikhin technique. Two types of derivatives of Lyapunov functions are used. Some examples are given to illustrate the introduced definitions and results.

Asymptotic behavior of a three-species food chain model with time-varying delays

In this paper, a stochastic three-species food chain model with time-varying delays is focussed. The existence and the asymptotic behavior of global positive solutions to the model are discussed, and the sufficient conditions for the 1th moment practical exponential stability and the extinction of the model are given by using the Razumikhin technique and Lyapunov method.

Global uniform asymptotical stability for fractional-order gene regulatory networks with time-varying delays and structured uncertainties

In this paper, we investigate a class of fractional-order gene regulatory networks with time-varying delays and structured uncertainties (UDFGRNs). First, we deduce the existence and uniqueness of the equilibrium for the UDFGRNs by using the contraction mapping principle. Next, we derive a novel global uniform asymptotic stability criterion of the UDFGRNs by using a Lyapunov function and the Razumikhin technique, and the conditions relating to the criterion depend on the fractional order of the UDFGRNs. Finally, we provide two numerical simulation examples to demonstrate the correctness and usefulness of the novel stability conditions. One of the most interesting findings is that the structured uncertainties indeed have an impact on the stability of the system.

Finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks

This paper mainly concerns with the finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks (FQVMNNs). First, the FQVMNNs are studied by separating the system into four real-valued parts owing to the noncommutativity of quaternion multiplication. Then, two state feedback control schemes, which include linear part and discontinuous part, are designed to guarantee that the synchronization of the studied networks can be achieved in finite time. Meanwhile, in terms of the stability theorem of delayed fractional-order systems, Razumikhin technique and comparison principle, some novel criteria are derived to confirm the synchronization of the studied models. Furthermore, two methods are used to obtain the estimation bounds of settling time. Finally, the feasiblity of the synchronization methods in quaternion domain is validated by the numerical examples.

Stability of delayed switched systems via Razumikhin technique and application to switched neural networks

This paper investigates the globally exponential stability of delayed switched systems via Razumikhin technique. According to mode-dependent dwell average time and multiple Lyapunov functions, new Razumikhin-type stability results are deduced. In contrast to the existing Rzumikhin-type results, the proposed ones are less conservative. In order to demonstrate the applicability, some stability and stabilization results for switched neural networks with time-varying delays are also derived. Several numerical examples are also employed to show the effectiveness and superiority of the obtained results.

On uniform asymptotic stability for nonlinear integro-differential equations of Volterra type

The specifics of the application of Razumikhin technique to the stability analysis of Volterra type integrodifferential equations are considered. The equation can be nonlinear and nonautonomous. We propose new sufficient conditions for uniform asymptotic stability of the zero solution using the phase space of a special construction and constraints on the right side of the equation. In the presented constraints we can analyze stability, relying not only on the behavior of the auxiliary function along the solutions, but also on the properties of the so called limiting equations.

Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stability results for RIIDDS by using the Lyapunov function and Razumikhin technique. Unlike other studies, we show that the stability behavior of the random time impulses is faster than the fixed time impulses. Finally, two examples were studied for comparative results of fixed and random time impulses it shows by simulation.