In this paper, the problem of robust mixed H 2 / H ∞ control is studied for an uncertain wireless sensor network (WSN) systems with random time delay, packet loss and sensor faults. A system model is established based on the characteristics of uncertain time delay and packet loss in WSN. In this model, system uncertainties are represented by random time delay and stochastic packet loss, which are described by a Markov chain. By using a Lyapunov-Krasovskii function, a mode-dependent mixed H 2 / H ∞ controller is designed to guarantee both the stochastic stability of the closed-loop system and the prescribed H 2 , H ∞ control performances. The sufficient conditions for the existence of the controller are proved by a series of Linear Matrix Inequalities (LMIs). If these LMIs are feasible, the mode-dependent mixed H 2 / H ∞ controller can be obtained. Matlab LMI toolbox is used to calculate the control law. Finally, a numerical example and its simulation results demonstrated the effectiveness of the proposed method.

中文翻译：

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具有时延和丢包的不确定无线传感器网络系统的鲁棒混合 H2/H∞ 控制

本文研究了具有随机时延、丢包和传感器故障的不确定无线传感器网络(WSN)系统的鲁棒混合H 2 / H ∞ 控制问题。基于WSN中不确定时延和丢包的特点，建立了系统模型。在该模型中，系统不确定性由随机时延和随机丢包表示，用马尔可夫链描述。通过使用Lyapunov-Krasovskii 函数，设计了一个模态相关混合H 2 / H ∞ 控制器，以保证闭环系统的随机稳定性和规定的H 2 , H ∞ 控制性能。控制器存在的充分条件由一系列线性矩阵不等式 (LMI) 证明。如果这些 LMI 是可行的，则可以得到与模式相关的混合 H 2 / H ∞ 控制器。Matlab LMI 工具箱用于计算控制律。最后，一个数值例子及其仿真结果证明了所提出方法的有效性。