Pinning-controlled synchronization of partially coupled dynamical networks via impulsive control

<abstract><p>In this paper, global exponential outer synchronization of coupled nonlinear systems with general coupling matrices are investigated via pinning impulsive control. More realistic and more general partially coupled drive-response systems are established, where the completely communication channel matrix between coupled nodes may not be a permutation matrix. By using pinning impulsive strategy involving pinning ratio and our generalised lower average impulsive interval method, a number of novel and less restrictive synchronization criteria are proposed. In the end, a numerical example is constructed to indicate the effectiveness of our theoretical results.</p></abstract>

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results