-
摘要: 研究了状态依赖广义时变脉冲系统的时域稳定问题.基于微分矩阵不等式 (Differential matrix inequalities, DMI) 和S-procedure理论, 给出了两类状态依赖广义时变脉冲系统时域稳定的充分条件.接下来, 根据给出的充分条件设计了状态反馈控制器, 使得闭环系统时域稳定.最后, 给出数值算例来验证结论的有效性.Abstract: This paper deals with the state-dependent finite-time stability problem for continuous-time linear time-varying descriptor impulse systems. The sufficient conditions for state-dependent continuous-time linear time-varying descriptor impulse systems to be finite-time stable are proposed in terms of a set of differential matrix inequalities (DMI) and the S-procedure arguments. Based on the conditions above, a state feedback controller is designed such that the resultant closed-loop system is finite-time stable. Finally, an example is presented to show the effectiveness of the obtained theoretical results.
-
[1] Duan G R. Analysis and Design of Descriptor Linear Systems. New York:Springer Verlag, 2010. [2] Rosenbrock H H. Structural properties of linear dynamical systems. International Journal of Control, 1974, 20(2):191-202 doi: 10.1080/00207177408932729 [3] Jeung E T, Kim J H, Park H B. H∞-output feedback controller design for linear systems with time-varying delayed state. IEEE Transactions on Automatic Control, 1998, 43(7):971-974 doi: 10.1109/9.701103 [4] Campell S L, Petzold L R. Canonical forms and solvable singular systems of differential equations. SIAM Journal of Algebraic Discrete Methods, 1983, 4(4):517-521 doi: 10.1137/0604051 [5] Takaba K, Morihira N, Katayama T. H∞ control for descriptor systems-a J-spectral factorization approach. In:Proceedings of the 33rd IEEE Conference on Decision and Control. Lake Buena Vista, USA:IEEE, 1994, 3:2251-2256 [6] Zhao Z H, Zhang Q L, Liu X D. H∞ control and parametric controllers for descriptor systems. In:Proceedings of the 2002 American Control Confernece. Anchorage, USA:IEEE, 2002, 6:4908-4913 [7] 苏晓明, 吕明珠.广义不确定周期时变系统的鲁棒稳定性分析.自动化学报, 2006, 32(4):481-488 http://www.aas.net.cn/CN/abstract/abstract14387.shtmlSu Xiao-Ming, Lv Ming-Zhu. Analysis of robust stability for linear time-varying uncertain periodic descriptor systems. Acta Automatica Sinica, 2006, 32(4):481-488 http://www.aas.net.cn/CN/abstract/abstract14387.shtml [8] 苏晓明, 王刚, 吕明珠.广义不确定周期时变系统的鲁棒镇定控制.东北大学学报 (自然科学版), 2006, 27(7):716-719 http://www.cnki.com.cn/Article/CJFDTOTAL-DBDX200607003.htmSu Xiao-Ming, Wang Gang, Lv Ming-Zhu. Robust stabilization control for generalized periodically time-varying uncertain descriptor systems. Journal of Northeastern University (Natural Science), 2006, 27(7):716-719 http://www.cnki.com.cn/Article/CJFDTOTAL-DBDX200607003.htm [9] 王刚, 苏晓明, 孟飞.一般广义时变系统的容许性和二次容许性.控制与决策, 2014, 29(2):221-225 http://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201402005.htmWang Gang, Su Xiao-Ming, Meng Fei. Admissibility and quadratic admissibility for time-varying general singular system. Control and Decision, 2014, 29(2):221-225 http://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201402005.htm [10] 艾玲.线性时变广义系统的脉冲控制.哈尔滨理工大学学报, 2004, 9(4):119-121 http://www.cnki.com.cn/Article/CJFDTOTAL-HLGX200404032.htmAi Ling. Impulse controllability of linear time-varying singular systems. Journal of Harbin University of Science and Technology, 2004, 9(4):119-121 http://www.cnki.com.cn/Article/CJFDTOTAL-HLGX200404032.htm [11] Kamenkov G V. On stability of motion over a finite interval of time. Akad Nauk SSSR Prikl Mat Meh, 1953, 17:529-540 [12] Dorato P. Short-time Stability in Linear Time-Varying Systems, Polytechnic Inst of Brooklyn N Y Microwave Research Inst, 1961. [13] Kablar N A. Finite-time stability of time-varying linear singular systems. In:Proceedings of the 37th IEEE Conference on Decision and Control. Tampa, USA:IEEE, 1998, 4:3831-3836 [14] Garcia G, Tarbouriech S, Bernussou J. Finite-time stabilization of linear time-varying continuous systems. IEEE Transactions on Automatic Control, 2009, 54(2):364-369 doi: 10.1109/TAC.2008.2008325 [15] Amato F, Ariola M, Cosentino C. Finite-time stability of linear time-varying systems:analysis and controller design. IEEE Transactions on Automatic Control, 2010, 55(4):1003-1008 doi: 10.1109/TAC.2010.2041680 [16] Liu L, Sun J T. Finite-time stabilization of linear systems via impulsive control. International Journal of Control, 2008, 81(6):905-909 doi: 10.1080/00207170701519060 [17] 孙继涛.脉冲系统的分析与控制.北京:科学出版社, 2013.Sun J T. Analysis and Control of Impulsive System. Beijing:Science Press, 2013. [18] Tong Y X, Wu B W, Huang F. Finite-time boundedness and L2-gain analysis for linear time-varying singular impulsive systems. In:Proceedings of the 24th Chinese Control and Decision Conference. Taiyuan, China:IEEE, 2012. 4031-4035 [19] Amato F, Ariola M, Dorato P. Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica, 2001, 37(9):1459-1463 doi: 10.1016/S0005-1098(01)00087-5 [20] Feng J E, Wu Z, Sun J B. Finite-time control of linear singular systems with parametric uncertainties and disturbances. Acta Automatica Sinica, 2005, 31(4):634-637 [21] Zhao S W, Sun J T, Liu L. Finite-time stability of linear time-varying singular systems with impulsive effects. International Journal of Control, 2008, 81(11):1824-1829 doi: 10.1080/00207170801898893 [22] Xu J, Sun J. Finite-time stability of linear time-varying singular impulsive systems. IET Control Theory and Applications, 2010, 4(10):2239-2244 doi: 10.1049/iet-cta.2010.0242 [23] Amato F, Ambrosino R, Ariola M, Cosentino C. Finite-time stability of linear time-varying systems with jumps. Automatica, 2009, 45(5):1354-1358 doi: 10.1016/j.automatica.2008.12.016 [24] Amato F, Ambrosino R, Ariola M, Calabrese F, Cosentino C. Finite-time stability of linear time-varying systems with jumps:analysis and controller design. In:Proceeding of the 2008 American Control Conference. Seattle, USA:IEEE, 2008. 1638-1643 [25] Ambrosino R, Calabrese F, Cosentino C, De Tommasi G. Sufficient conditions for finite-time stability of impulsive dynamical systems. IEEE Transactions on Automatic Control, 2009, 54(4):861-865 doi: 10.1109/TAC.2008.2010965 [26] Amato F, Ambrosino R, Cosentino C, De Tommasi G. Finite-time stabilization of impulsive dynamical linear systems. Nonlinear Analysis:Hybrid Systems, 2011, 5(1):89-101 doi: 10.1016/j.nahs.2010.10.001 [27] Amato F, Ambrosino R, Ariola M, De Tommasi G. Robust finite-time stability of impulsive dynamical linear systems subject to norm-bounded uncertainties. International Journal of Robust and Nonlinear Control, 2011, 21(10):1080-1092 doi: 10.1002/rnc.1620 [28] Amato F, De Tommasi G, Pironti A. Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems. Automatica, 2013, 49(8):2546-2550 doi: 10.1016/j.automatica.2013.04.004 [29] Amato F, Ambrosino R, Ariola M, Cosentino C, De Tommasi G. Finite-Time Stability and Control. London:Springer-Verlag, 2014. [30] Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia, USA:SIAM, 1994. [31] 苏晓明, 阿迪亚.广义时变脉冲系统的输入输出时域稳定.自动化学报, 2014, 40(11):2512-2520 http://www.aas.net.cn/CN/abstract/abstract18527.shtmlSu Xiao-Ming, Adiya. Input-output finite-time stability of linear time-varying descriptor impulse systems. Acta Automatica Sinica, 2014, 40(11):2512-2520 http://www.aas.net.cn/CN/abstract/abstract18527.shtml -
下载:
图(1)
计量
- 文章访问数: 2047
- HTML全文浏览量: 211
- PDF下载量: 851
- 被引次数: 0
