Partial stability analysis of some classes of nonlinear systems

A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.     

具有输入饱和因子的滞后关联大系统的分散控制

研究了一类具有饱和因子的滞后关联大系统的分散控制问题.首先对饱和因子进行了巧妙地处理,再通过构造Lyapunov泛函,利用(LMI)方法给出了分散控制状态反馈控制器的设计方法.控制器通过解线性矩阵不等式即可得到,计算简便.最后,数值例子和仿真说明了该设计方法的有效性.     

电力系统中的非同期合闸产生过电压控制模型研究

本文首先建立了电力系统中非同期合闸过电压的时延控制系统的数学西模型,得到了相应闭环系统的稳定性以及振动性,同时利用时延控制次优控制的灵敏度系数研究者到了该系统的次优控制设计方法及相应的次优控制设计过程,最后我们结合采样数据,利用泛函微分方程的分布迭代方法进行数值计算,得到了均优于已有文献的结果。     

Fully Data-Driven Time-Delay Interferometry with Time-Varying Delays

Raw space-based gravitational-wave data like laser interferometer space antenna's (LISA) phase measurements are dominated by laser frequency noise. The standard technique to make this data usable for gravitational-wave detection is time-delay interferometry (TDI), which cancels laser noise terms by forming suitable combinations of delayed measurements. To do so, TDI relies on inter-spacecraft distances and on how laser noise enters the interferometric data. The basic concepts of an alternative approach which does not rely on independent knowledge of temporal correlations in the dominant noise recently introduced. Instead, this automated principal component interferometry (aPCI) approach only assumes that one can produce some linear combinations of the temporally nearby regularly spaced phase measurements, which cancel the laser noise. Then the data is let to reveal those combinations, thus providing a set of laser-noise-free data channels. The authors' previous approach relies on the simplifying additional assumption that the filters which lead to the laser-noise-free data streams are time-independent. In LISA, however, these filters will vary as the constellation armlengths evolve. Here, a generalization of the basic aPCI concept compatible with data dominated by a still unmodeled but slowly varying dominant noise covariance is discussed. Despite its independence on any model, aPCI successfully mitigates laser frequency noise below the other noises' level, and its sensitivity to gravitational waves is the same as the state-of-the-art second-generation TDI, up to a 2% error.     

Autapse-induced target wave,spiral wave in regular network of neurons

Autapse is a type of synapse that connects axon and dendrites of the same neuron, and the effect is often detected by close-loop feedback in axonal action potentials to the owned dendritic tree. An artificial autapse was introduced into the Hindmarsh-Rose neuron model, and a regular network was designed to detect the regular pattern formation induced by autapse. It was found that target wave emerged in the network even when only a single autapse was considered. By increasing the(autapse density) number of neurons with autapse, for example, a regular area(2×2, 3×3, 4×4, 5×5 neurons) under autapse induced target wave by selecting the feedback gain and time-delay in autapse. Spiral waves were also observed under optimized feedback gain and time delay in autapses because of coherence-like resonance in the network induced by some electric autapses connected to some neurons. This confirmed that the electric autapse has a critical role in exciting and regulating the collective behaviors of neurons by generating stable regular waves(target waves, spiral waves) in the network. The wave length of the induced travelling wave(target wave, spiral wave), because of local effect of autapse, was also calculated to understand the waveprofile in the network of neurons.     

Near-optimum design of nonstationary linear systems with state and control delays

A computationally efficient method based on a sensitivity approach is developed to obtain suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. The proposed suboptimal control includes some truncated series whose terms are calculated in a recursive manner from nondelay system optimization.     

一类不确定时滞系统的鲁棒稳定性

给出了不确定时滞系统鲁棒稳定的若干结果,同时讨论了这类系统的稳定度,改进了前人关于时滞系统稳定性和鲁棒稳定性的一些结论,并给出了应用的例子。     

多重边复杂网络系统的稳定性分析

根据网络中边的不同性质提出了网络拆分的思想,通过引入时滞进行拆分,从而建立了多重边复杂网络的动力学模型. 基于Lyapunov稳定理论研究了多重边复杂网络的稳定性问题,给出了节点动力学无时滞和有时滞两种情况下网络稳定的充分条件. 最后通过数值仿真验证了结论的正确性和有效性.     

水资源时延控制模型及研究

水资源系统是由水资源自然分系统和人工分系统合成的复杂大系统.把设计修建的水资源工程视作安装于自然系统上的一个控制器,同时考虑当前状态量与时延量的制约关系.首次建立了一个由流域、湖泊及引水工程等组成的非线性水资源时延控制数学模型,讨论了该类系统的稳定性、最优控制、次优控制等理论,最后给出次优控制的数值计算及结果.     

Exponential synchronization of complex networks with Markovian jump and mixed delays

In this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.