Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

Abstract

This paper considers the asymptotical synchronization and H ∞ synchronization for coupled neutral-type delay partial differential systems (NDPDSs). First, we construct a coupled synchronization error dynamic. Using the method of nonsingular matrix transformation, we decouple these coupled synchronization error dynamical systems. Then we study the asymptotical stability of the decoupled synchronization error dynamical systems through the Lyapunov-Krasovskii functional method, which implies the asymptotical synchronization of the coupled NDPDSs. Furthermore, when external disturbances enter the coupled NDPDSs, the H ∞ synchronization problem is also considered. The equivalence between the H ∞ stability of decoupled synchronization error dynamical systems and the H ∞ synchronization of coupled NDPDSs is proved by rigorous mathematical analysis. Then the criterion for the H ∞ stabilization is presented, which guarantees the H ∞ synchronization of the coupled NDPDSs. Moreover, as a remarkable difference between the ordinary differential systems and partial differential systems, the effect of the spatial domain on the synchronization is revealed through the obtained criteria. At last, numerical examples are given to illustrate the correctness of our results.

Delay Partial Synchronization of Mutual Delay Coupled Boolean Networks

“…Synchronization is a basic characteristic of the complex systems, which exists in natural and artificial systems. 15 In past years, there were other research results, for example, synchronization of neural networks via pinning control, [16][17][18] function projective synchronization of the complex networks, [19][20][21] outer synchronization between two hybrid-coupled delayed networks, 22 synchronization of the delay partial differential systems with coupled neutral-type, 23 synchronization of the systems with different orders, 24 and robust synchronization control for chaotic systems with fractional-order. 25 With the rapid development of the system biology, BN is one of the important models for studying biological system and gene regulation network.…”

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

“…One is the dynamic characteristic governed by partial differential equations; another is the static characteristic embodied by algebraic constraints, whereas the normal system without the static attribute. Although there are a variety of research results about singular systems [6][7][8] and distributed parameter systems, [9][10][11][12][13][14] some issues for SDPSs were investigated (e.g. analytical solution, 5,15 controllability and observability, 16 passivity criteria, see Reis and Jacob 17 and references therein).…”

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

“…These phenomena are generally modeled in partial differential systems (PDSs). Therefore, increasing concerns have risen on the study of PDSs [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. A significant part of research is based on reaction-diffusion neural network models, such as [25,[34][35][36][37][38].…”

“…The synchronization of complex partial differential systems has also yielded fruitful research results [25][26][27][28][29][39][40][41][42][43]. Some of the studies have been based on networks without time delay, in which the spatial variables are onedimensional, such as [26][27][28].…”

“…Hence, the problem of considering time delay in the PDSs has aroused the interest of researchers. In [29], sufficient conditions on asymptotical synchronization for a class of coupled time-delay PDSs via boundary control have been obtained; Wu et al address the robust ∞ synchronization of PDSs with time delay [41,42]; Wang et al focus on the passivity problem of a class of delayed reaction-diffusion networks [43].…”