Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays

Abstract

This paper studies the problem of non-fragile synchronization control for Markovian jumping complex dynamical networks with probabilistic time-varying coupling delays. By constructing a new Lyapunov-Krasovskii functional (LKF) and combining the reciprocal convex technique, sufficient conditions for the complex dynamical networks to be globally asymptotically synchronized in the mean square sense are derived. The probability distribution of the delays have been proposed and delay probability-distribution-dependent conditions are derived in the form of linear matrix inequalities (LMIs). The derived conditions depend not only on the size of the delay but also on the probability of the delay taking values in some intervals. Further, a non-fragile synchronization controller is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.

Finite-Time Stability of Uncertain Nonlinear Systems with Time-Varying Delay

“…then the linear system is finite-time stable with control input ( ) in (5), and the finite time is estimated by…”

“…In recent years, the stability problem of linear systems has been well addressed [1,2]. Some results of nonlinear systems with time-varying delay can be found in [3][4][5][6][7][8][9] and the references therein. On the other hand, parameter uncertainties cannot be avoided in a control system due to modeling errors, external disturbances, and linearization approximations, which are the main causes of instability and poor performance of control systems.…”

Synchronization of Uncertain Complex Networks with Time‐Varying Node Delay and Multiple Time‐Varying Coupling Delays

“…Particularly, different types of time-delay such as node delay, coupling delay, distributed delay, and hybrid delay have been developed [23][24][25][26]. Furthermore, the value of the time-delay can be frequently varied, which is called time-varying delays [27][28][29]. Thus, the synchronization of complex networks with uncertain couplings and time-varying delays is well worth studying.…”

New Methods of Finite‐Time Synchronization for a Class of Fractional‐Order Delayed Neural Networks

“…Some important results on finitetime synchronization were demonstrated on integer-order systems [24][25][26][27][28]. Note that time delay [29][30][31] occurs in many physical and engineering systems. So it is natural to study fractional-order systems with delays.…”