Stability analysis of linear fractional differential system with multiple time delays
Stability analysis of linear fractional differential system with multiple time delays
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时滞非线性分数阶微分系统的李雅普诺夫方法
DOI：
10.1007/s11071
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发表时间：
2007-06-01
影响因子：
5.6
通讯作者：
Lu, Jinhu
中科院分区：
文献类型：
--
作者：
Deng, Weihua;Li, Changpin;Lu, Jinhu
本文研究了一类具有时滞的n维线性分数阶微分方程的稳定性，其中时滞矩阵定义在（R+）（nxn）中。利用拉普拉斯变换，我们引入了上述多时滞系统的特征方程。我们发现，如果特征方程的所有根都有负部分，则上述分数阶线性系统的平衡点是Lyapunov全局渐近稳定的，如果平衡点存在，则该平衡点与经典微分方程的平衡点几乎相同。作为一种应用，我们将该定理应用于Chen和Moore[非线性动力学29,2002,191]研究的一维时滞系统，并确定了系统的渐近稳定区域。我们还利用线性反馈控制方法和我们的定理处理了耦合时滞Duffing振子之间的同步问题，其中确定了控制同步参数的定义域。
In this paper, we study the stability of n-dimensional linear fractional differential equation with time delays, where the delay matrix is defined in (R+)(nxn). By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. As its an application, we apply our theorem to the delayed system in one spatial dimension studied by Chen and Moore [Nonlinear Dynamics 29, 2002, 191] and determine the asymptotically stable region of the system. We also deal with synchronization between the coupled Duffing oscillators with time delays by the linear feedback control method and the aid of our theorem, where the domain of the control-synchronization parameters is determined.