Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India.
Istanbul University-Cerrahpasa, Faculty of Engineering, Department of Computer Engineering, 34320 Avcilar, Istanbul, Turkey.
Neural Netw. 2019 Jun;114:28-37. doi: 10.1016/j.neunet.2019.02.004. Epub 2019 Feb 22.
This paper investigates state estimation for complex dynamical networks (CDNs) with time-varying delays by using sampled-data control. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling state estimator is transformed into a continuous time-delay system with stochastic parameters in the system matrices, where the purpose is to design a state estimator to estimate the network states through available output measurements. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) containing triple and fourth integral terms and applying Wirtinger-based single and double integral inequality, Jenson integral inequality technique, delay-dependent stability conditions are established. The obtained conditions can be readily solved by using the LMI tool box in MATLAB. Finally, a numerical example is provided to demonstrate the validity of the proposed scheme.
本文研究了利用采样数据控制对具有时变时滞的复杂动态网络（CDN）进行状态估计的问题。为了简化技术开发，仅考虑两种不同的采样周期，其发生概率为常数并满足伯努利分布，这可以进一步扩展到具有多个随机采样周期的情况。通过应用输入时滞方法，将概率采样状态估计器转换为具有随机参数的连续时滞系统，系统矩阵中的目的是通过可用的输出测量设计状态估计器来估计网络状态。通过构造一个包含三部分和四部分积分项的适当的 Lyapunov-Krasovskii 泛函（LKF），并应用基于 Wirtinger 的单积分和双积分不等式、Jensen 积分不等式技术，建立了时滞相关稳定性条件。所得到的条件可以通过使用 MATLAB 中的 LMI 工具箱方便地求解。最后，提供了一个数值示例来验证所提出方案的有效性。
