Adaptive synchronisation for a class of output‐coupling complex networks with output feedback nodes

Fixed-Time and Finite-Time Synchronization for a Class of Output-Coupling Complex Networks via Continuous Control

“…Specifically, Example 1 is given to verify Theorem 1 and Example 2 is provided to illustrate Theorem 2. Now, we consider the following two-dimensional van der pol system [21] which is presented as:…”

“…We will control the CNs (18) under controllers (21) such that it will be synchronized onto the following target state within finite time:…”

“…From the analysis of [21], for the function ( ) = = = , we get 0 0.071 T = . Figure 1, Figure 2 show the time response of error systems without control and Figure 3 and Figure 4 present that the synchronization is achieved in finite time.…”

“…From the viewpoint of coupling among nodes, complex networks mainly be divided into two representative types, that is, output-coupling complex networks and state-coupling complex networks. In [21], global asymptotic adaptive synchronization problem for a class of output-coupling complex networks was studied by employing adaptive dynamical output feedback controllers. In recent years, most of researches focus on state-coupling complex networks while output-coupling complex networks attracts relatively less attention let alone research on fixed-time and finite-time synchronization problems.…”