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### 具有混合时变时滞的2-D离散时间非线性切换系统的H∞控制问题研究

1. 燕山大学理学院, 秦皇岛 066004
• 收稿日期:2022-04-11 修回日期:2022-05-16 发布日期:2022-11-04
• 通讯作者: 彭丹,Email:dpeng1219@163.com.
• 基金资助:
河北省省级科技计划资助(F2020203037),国家自然科学基金杰青项目(61825304),河北省自然科学基金创新研究群体项目(F2020203013)资助课题.

LIU Mengjie, PENG Dan. Study of H Control Problem for 2-D Discrete-Time Nonlinear Switched Systems with Mixed Time-Varying Delays[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(10): 2774-2793.

### Study of H∞ Control Problem for 2-D Discrete-Time Nonlinear Switched Systems with Mixed Time-Varying Delays

LIU Mengjie, PENG Dan

1. School of Science, Yanshan University, Qinhuangdao 066004
• Received:2022-04-11 Revised:2022-05-16 Published:2022-11-04

In this paper,we study the H control problem of two-dimensional (2-D) discrete-time nonlinear switched systems with mixed time-varying delays based on the Roesser model.Firstly,an improved Lyapunov function is implemented by introducing some sum of state vectors containing both single and double forms,so as to strive to obtain additional information related to the time delays.Secondly,a 2-D admissible edge-dependent average dwell time (2AED-ADT) method for 2-D discrete-time nonlinear switched systems is introduced.Using this method,sufficient conditions are given by the linear matrix inequalities (LMIs) to guarantee the exponential stability and H performance of the 2-D discrete-time nonlinear switched systems.Further,based on the above stability results,a dynamic output feedback (DOF) controller is designed to stabilize the nonlinear closed-loop switched systems with H performance index γ.Finally,the superiority and validity of the obtained results are verified by two numerical calculation examples.

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