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Robust Mixed H2/H∞ Control for an Uncertain Wireless Sensor Network Systems with Time Delay and Packet Loss

Yuanbo Shi*, Jianhui Wang, Xiaoke Fang, Yueyang Huang, and Shusheng Gu
International Journal of Control, Automation, and Systems, vol. 19, no. 1, pp.88-100, 2021

Abstract : In this paper, the problem of robust mixed H2/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 H2/H∞ controller is designed to guarantee both the stochastic stability of the closed-loop system and the prescribed H2, 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 H2/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.

Keyword : Linear matrix inequalities (LMIs), Markov chain, mixed H2/H∞ control, time delay and packet loss, uncertain

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