• • 上一篇    

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

刘梦洁, 彭丹   

  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.

刘梦洁, 彭丹. 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[J]. 系统科学与数学, 2022, 42(10): 2774-2793.

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
文章基于Roesser模型,研究了具有混合时变时滞的二维(2-D)离散时间非线性切换系统的H控制问题.首先,选取改进的Lyapunov函数,该函数包含单形式和双形式状态的和,以此来获得额外时滞相关的信息.其次,介绍了一种针对2-D离散时间非线性切换系统的2-D允许边缘相关的平均驻留时间(2AED-ADT)方法.利用该方法由线性矩阵不等式(LMIs)给出了保证2-D离散时间非线性切换系统指数稳定并具有H性能的充分条件.进而,根据上述稳定性结果,设计了一种动态输出反馈(DOF)控制器,来稳定非线性闭环切换系统,使其具有H性能指标γ.最后,通过两个数值算例验证了所得结果的的优越性和有效性.
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.

MR(2010)主题分类: 

()
[1] Kaczorek T. Two-Dimensional Linear Systems. Berlin:Springer-Verlag, 1985.
[2] 陈东彦,于浍.状态饱和2-D离散系统的稳定性分析.系统科学与数学, 2014, 34(2):171-178.(Chen D Y, Yu H. Stability analysis of 2-D discrete systems with state saturation. Journal of Systems Science and Mathematical Sciences, 2014, 34(2):171-178.)
[3] Roesser R. A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 1975, 20(1):1-10.
[4] Fornasini E, Marchesini G. Doubly-indexed dynamical systems:State-space models and structural properties. Theory of Computing Systems, 1978, 12(1):59-72.
[5] Yang R N, Zheng W X, Yu Y. Event-triggered sliding mode control of discrete-time twodimensional systems in Roesser model. Automatica, 2020, 114(5):108813.
[6] Ahn C K, Wu L, Shi P. Stochastic stability analysis for 2-D Roesser systems with multiplicative noise. Automatica, 2016, 69:356-363.
[7] Dami L, Benhayoun M, Benzaouia A. Admissibility and stabilization of singular continuous 2D systems described by Roesser model. Multidimensional Systems and Signal Processing, 2020, 31(2):673-687.
[8] Peng D, Nie H M. Stabilisation for 2-D discrete-time switched nonlinear systems with mixed time-varying delays under all modes unstable. International Journal of Systems Science, 2022, 53(4):757-777.
[9] Peng D, Xu H S. A novel approach to delay-variation-dependent stability analysis of 2-D discretetime systems with mixed delays. IEEE Access, 2019, 7:99817-99829.
[10] Benzaouia A, Hmamed A, Tadeo F. Stability conditions for discrete 2D switching systems, based on a multiple Lyapunov function. 2009 European Control Conference (ECC), 2009, 2706-2710.
[11] Benzaouia A, Hmamed A, Tadeo F, et al. Stabilisation of discrete 2D time switching systems by state feedback control. Journal of the Franklin Institute, 2011, 42(3):479-487.
[12] Shi S, Ma Y J R, Ren S Q. Asynchronous filtering for 2-D switched systems with missing measurements. Multidimensional Systems and Signal Processing, 2018, 30(2):543-560.
[13] Duan Z X, Xiang Z R. State feedback H∞ control for discrete 2D switched systems. Journal of the Franklin Institute, 2013, 350(6):1513-1530.
[14] Duan Z X, Ghous I, Xia Y Q, et al. H∞ control problem of discrete 2-D switched mixed delayed systems using the improved Lyapunov-Krasovskii functional. International Journal of Control Automation and Systems, 2020, 18(8):2075-2087.
[15] Duan Z X, Xiang Z R. Output feedback H∞ stabilization of 2D discrete switched systems in FM LSS model. Circuits, Systems, and Signal Processing, 2014, 33(4):1095-1117.
[16] Huang S P, Xiang Z R. Delay-dependent stability for discrete 2D switched systems with state delays in the Roesser model. Circuits Systems&Signal Processing, 2013, 32(6):2821-2837.
[17] Fei Z Y, Shi S, Zhao C, et al. Asynchronous control for 2-D switched systems with mode-dependent average dwell time. Automatica, 2017, 79:198-206.
[18] Gao L J, Cao Z B, Zhang M, et al. Input-to-state stability for hybrid delayed systems with admissible edge-dependent switching signals. Journal of the Franklin Institute, 2020, 357:8823-8850.
[19] Liu H Y, Gao L J, Wang Z Y, et al. Asynchronous l2-l filtering of discrete-time impulsive switched systems with admissible edge-dependent average dwell time switching signal. International Journal of Systems Science, 2021, 52(8):1564-1585.
[20] Hien L V, Vu L H, Trinh H. Stability of two-dimensional descriptor systems with generalized directional delays. Systems&Control Letters, 2018, 112:42-50.
[21] Hien L V, Trinh H. Switching design for suboptimal guaranteed cost control of 2-D nonlinear switched systems in the Roesser model. Nonlinear Analysis:Hybrid Systems, 2017, 24:45-57.
[22] Wang J, Liang J, Dobaie A M. Dynamic output-feedback control for positive Roesser system under the switched and TS fuzzy rules. Information Sciences, 2018, 422:1-20.
[23] Xu H, Zou Y, Lu J, et al. Robust H∞ control for a class of uncertain nonlinear two-dimensional systems with state delays. Journal of the Franklin Institute, 2005, 342(7):877-891.
[24] Hua C C, Liu G P, Guan X P. Switching regulation based stabilisation of discrete-time 2D switched systems with stable and unstable modes. IET Control Theory&Applications, 2018, 12(7):953-960.
[25] Duan Z X, Xiang Z R, Karimi H R. Delay-dependent H∞ control for 2-D switched delay systems in the second FM model. Journal of the Franklin Institute, 2013, 350(7):1697-1718.
[26] Hien L V, Trinh H. Stability of two-dimensional Roesser systems with time-varying delays via novel 2D finite-sum inequalities. IET Control Theory&Applications, 2016, 10(14):1665-1674.
[27] Peng D, Hua C C. Improved approach to delay-dependent stability and stabilisation of twodimensional discrete-time systems with interval time-varying delays. IET Control Theory&Applications, 2015, 9(12):1839-1845.
[28] Fridman E, Shaked U. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control, 2002, 47(11):1931-1937.
No related articles found!
阅读次数
全文


摘要