论文标题
具有网络同步应用的延迟系统的自适应有限时间稳定性
Adaptive Finite Time Stability of Delayed Systems With Applications to Network Synchronization
论文作者
论文摘要
迄今为止，还没有设置延迟系统的有限时间稳定性（FNTSTA）理论。在本文中，我们提出了一个两个倍方法（下午2点），以实现此对象。在第一阶段，我们证明了系统误差规范从初始值演变为1的时间是有限的。然后，在第二阶段，我们证明了从1到0的误差的时间也是有限的，因此获得了FNTSTA。考虑到控制器的成本和复杂性，我们仅使用两个简单的术语来实现此目标。对于拟议的下午2点，时间延迟可以是相同的或异步的，有限的或无限的，等等。规范可以是$ 2 $ -NORM，$ 1 $ -NORM，$ \ infty $ -NORM，这表明下午2点功能强大，并且具有广泛的应用程序范围。此外，我们还证明了使用2pm的延迟系统理论的自适应有限时间稳定性（AFNTSTA）。作为获得的FNTSTA理论的应用，我们认为对于具有异步无限时间延迟的复杂网络的有限时间外同步（FNTOSYN），还获得了相应的标准。最后，给出了两个数值示例以证明我们理论的有效性。
The finite time stability (FnTSta) theory of delayed systems has not been set up until now. In this paper, we propose a two-phases-method (2PM), to achieve this object. In the first phase, we prove that the time for norm of system error evolving from initial values to 1 is finite; then in the second phase, we prove that the time for norm of the error evolving from 1 to 0 is also finite, thus FnTSta is obtained. Considering the cost and complexity of controller, we use only two simple terms to realize this aim. For the proposed 2PM, time delays can be the same or asynchronous, bounded or unbounded, etc; the norm can be $2$-norm, $1$-norm, $\infty$-norm, which show that 2PM is powerful and has a wide scope of applications. Furthermore, we also prove the adaptive finite time stability (AFnTSta) theory of delayed systems using 2PM. As an application of the obtained FnTSta theory, we consider the finite time outer synchronization (FnTOSyn) for complex networks with asynchronous unbounded time delays, corresponding criteria are also obtained. Finally, two numerical examples are given to demonstrate the validity of our theories.
