Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control.

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.