摘要本文主要讨论含有时变时滞的离散切换正系统的异步镇定性.首先,通过构造适当的Lyapunov-Krasovskii泛函,得到离散切换正时滞系统在模型依赖平均驻留时间(MDADT)切换信号下指数稳定的一个充分条件.其次,通过允许所构造的Lyapunov-Krasovskii泛函在被激活的子系统和控制器不匹配的时间区间内递增,基于MDADT切换信号,得到存在一类状态反馈控制器使得闭环系统在异步切换下是正的且是指数稳定的一些充分条件.最后,给出两个数值例子说明所提出方法的有效性. | | 服务 | | | 加入引用管理器 | | E-mail Alert | | RSS | 收稿日期: 2014-08-18 | | 基金资助:国家自然科学基金(61403241),西安工程大学博士科研启动金(BS1619),陕西省教育厅(17JK0340),河南省科技厅基础与前沿计划(162300410076),河南省教育厅高等学校重点科研(16A110020)资助项目. |
引用本文: | 刘婷婷, 吴保卫, 刘丽丽, 王月娥. 离散切换正时滞系统在异步切换下的镇定性[J]. 应用数学学报, 2018, 41(6): 721-734. LIU Tingting, WU Baowei, LIU Lili, WANG Yue-E. Stabilization of Discrete Switched Positive Time-delay Systems Under Asynchronous Switching. Acta Mathematicae Applicatae Sinica, 2018, 41(6): 721-734. | | | | 链接本文: | http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2018/V41/I6/721 |
[1] | Farina L, Rinaldi S. Positive Linear Systems. New York:Wiley, 2000 | [2] | Kaczorek T. Positive 1D and 2D Systems. London:Springer-Verlag, 2002 | [3] | Plemmons R, Berman A. Nonnegative Matrices in the Mathematical Sciences. Philadelphia, PA:SIAM, 1979 | [4] | Shen J, Lam J. Static output-feedback stabilization with optimal L1-gain for positive linear systems.Automatica, 2016, 63:248-253 | [5] | Zhu S, Han Q L, Zhang C. l1-gain performance analysis and positive filter design for positive discretetime Markov jump linear systems:a linear programming approach. Automatica, 2014, 50(8):2098-2107 | [6] | Ebihara Y, Peaucelle D, Arzelier D. LMI approach to linear positive system analysis and synthesis. Systems & Control Letters, 2014, 63:50-56 | [7] | Haddad W, Chellaboina V. Stability theory for nonnegative and compartmental dynamical systems with time delays. Systems & Control Letters, 2004, 51(5):355-361 | [8] | Haddad W, Chellaboina V. Stability and dissipativity theory for nonnegative dynamic systems:a unified analysis framework for biological and physiological systems. Nonlinear Analysis:Real World Applications, 2005, 6(1):35-65 | [9] | Liu T T, Wu B W, Liu L L, Wang Y E. Finite-time stability of discrete switched singular positive systems. Circuits, Systems, and Signal Processing, 2017, 36(6):2243-2255 | [10] | Liu T T, Wu B W, Liu L L, Wang Y E. New stabilization results for discrete-time positive switched systems with forward mode-dependent average dwell time. Transactions of the Institute of Measurement and Control, 2017, 39(2):224-229 | [11] | Vu L, Kristi M. Stability of time-delay feedback switched linear systems. IEEE Transactions on Automatic Control, 2010, 55(10):2385-2389 | [12] | Fornasini E, Valcher M E. Asymptotic stability and stabilizability of special classes of discrete-time positive switched systems. Linear Algebra and its Applications, 2013, 438(4):1814-1831 | [13] | Liu T T, Wu B W, Tong Y X. Exponential stability of discrete-time linear singular positive time-delay systems. In:Proc. 27th Chinese Control and Decision Conference, Qingdao, 2015:6069-6073 | [14] | Wang Y E, Sun X M, Wang Z, Zhao J. Construction of Lyapunov-Krasovskii functionals for switched nonlinear systems with input delay. Automatica, 2014, 50(4):1249-1253 | [15] | Zhao X, Zhang L, Shi P. Stability of a class of switched positive linear time-delay systems. International Journal of Robust and Nonlinear Control, 2013, 23(5):578-589 | [16] | Xiang M, Xiang Z. Exponential stability of discrete-time switched linear positive systems with timedelay. Applied Mathematics and Computation, 2014, 230:193-199 | [17] | Liu X, Dang C. Stability analysis of positive switched linear systems with delays. IEEE Transactions on Automatic Control, 2011, 56(7):1684-1690 | [18] | Li S, Xiang Z, Karimi H. Stability and L1-gain controller design for positive switched systems with mixed time-varying delays. Applied Mathematics and Computation, 2013, 222(5):507-518 | [19] | Xie G, Wang L. Stabilization of switched linear systems with time-delay in detection of switching signal. Journal of Mathematical Analysis and Applications, 2005, 305(1):277-290 | [20] | Wang Y, Zhao J, Jiang B. Stabilization of a class of switched linear neutral systems under asynchronous switching. IEEE Transactions on Automatic Control, 2013, 58(8):2114-2119 | [21] | Zhang L X, Gao H. Asynchronously switched control of switched linear systems with average dwell time. Automatica, 2010, 46(5):953-958 | [22] | Liu T T, Wu B W, Liu L L, Wang Y E. Asynchronously finite-time control of discrete impulsive switched positive time-delay systems. Journal of the Franklin Institute, 2015, 352(10):4503-4514 | [23] | Wang Y E, Sun X M, Zhao J. Stabilization of a class of switched stochastic systems with time delays under asynchronous switching. Circuits, Systems & Signal Processing, 2013, 32(1):347-360 | [24] | Wang Y E, Sun X M, Zhao J. Asynchronous H∞ control of switched delay systems with average dwell time. Journal of the Franklin Institute, 2012, 349(10):3159-3169 | [25] | Xiang W, Xiao J. H∞ filtering for switched nonlinear systems under asynchronous switching. International Journal of Systems Science, 2011, 42(5):751-765 | [26] | Xiang W, Xiao J, Iqbal M N. State estimation for short-time switched linear systems under asynchronous switching. International Journal of Adaptive Control & Signal Processing, 2014, 28(6):553-561 | [27] | Wang R, Fei S. New stability and stabilization results for discrete-time switched systems. Applied Mathematics and Computation, 2014, 238:358-369 |
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