CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (6): 706-713.

CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS

蒋威

Department of Mathematics, University of Anhui, Hefei 230039, P. R. China

收稿日期:2002-01-30 修回日期:2003-01-10 出版日期:2003-06-18 发布日期:2003-06-18
基金资助:
the National Natural Science Foundation of China(10241005)

CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS

JIANG Wei

Department of Mathematics, University of Anhui, Hefei 230039, P. R. China

Received:2002-01-30 Revised:2003-01-10 Online:2003-06-18 Published:2003-06-18
Supported by:
the National Natural Science Foundation of China(10241005)

摘要/Abstract

摘要： The controllability of delay degenerate differential control systems is discussed. Firstly, delay degenerate differential control system was transformed to be canonical form, and the connected terms were gotten rid of, had delay degenerate differential control systems with independent subsystems. For the general delay degenerate differnetial control systems, it was gotten that the necessary and sufficient condition of that they are controllable is that their reachable set is equal to the whole space. For the delay degenerate differential control systems with independent subsystems, it was gotten that the necessary and sufficient conditions of that they are controllable are that their reachable sets are equal to their corresponding subspaces. Then some algebra criteria were gotten. Finally, an example was given to illustrate the main results.

Abstract: The controllability of delay degenerate differential control systems is discussed. Firstly, delay degenerate differential control system was transformed to be canonical form, and the connected terms were gotten rid of, had delay degenerate differential control systems with independent subsystems. For the general delay degenerate differnetial control systems, it was gotten that the necessary and sufficient condition of that they are controllable is that their reachable set is equal to the whole space. For the delay degenerate differential control systems with independent subsystems, it was gotten that the necessary and sufficient conditions of that they are controllable are that their reachable sets are equal to their corresponding subspaces. Then some algebra criteria were gotten. Finally, an example was given to illustrate the main results.

中图分类号:

O175.15

蒋威. CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(6): 706-713.

JIANG Wei. CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(6): 706-713.

参考文献

[1] ZHENG Zu-xiu.Theory of Functional Differential Equations[M].Hefei:Anhui Education Press, 1994.(in Chinese)
[2] Boyarinchev U E.Solution of Ordinary Differential Equations of Degenerate System[M]. Moscow:Science Press.1988.(in Russian)
[3] Campbell S L.Singular Systems of Differential Equation(Ⅱ)[M].San Francisco,London,Melbourne:Pitman,1982.
[4] Dai L.Singular Control Systems[M].London,Paris,Tokyo:Springer-Verlag,1989.
[5] Ronald B Zmood.The Euclidean space controllability of control systems with delay[J].SIAM J Control,1974,12(4):609-623.
[6] ZHANG Jin-shui.Singular System Economics Control Theory[M].Beijing:Tsinghua University Press,1990.(in Chinese)
[7] LIU Yong-qing,GUAN Zhi-hong.Theory and Application of Lagre-Scale Dynamic Systems (Vol.5):Stability,Stabilization and Control of Measure Large-Scale Systems with Impulses[M]. Guangzhou:South China University of Technology Press,1996.(in Chinese)
[8] JIANG Wei.The function-controllability of the nonlinear neutral control systems[J].Journal of Mathematical Study,1996,29(4):55-60.(in Chinese)
[9] JIANG Wei.The output controllability of linear system with delay[J].Ann Differential Equ ations, 1995,10(5):39-44.
[10] JIANG Wei,SONG Wen-zhong,FEI Su-min.The Function-Controllability of the Nonlinear Control Systems with State and Control Delay[M].London:World Scientific,2000,143-148.
[11] JIANG Wei,ZHENG Zu-xiu.The general solution for the degenerate differential system with delay[J].Acta Mathematica Sinia,1999,42(5):769-780.(in Chinese)
[12] JIANG Wei,ZHENG Zu-xiu.The constant variation formula and the general solution of degenerate neutral differential systems[J].Acta Mathematicae Applicatae Sinica,1998,21(4):562-570.(in Chinese)
[13] JIANG Wei,ZHENG Zu-xiu.On the degenerate differential systems with delay[J].Ann Differential Equations,1998,14(2):204-211.
[14] JIANG Wei,ZHENG Zu-xiu.The Solvability of the degenerate differential systems with delay[J]. Chinese Quarterly Journal of Mathematics,2000,15(3):1-7.
[15] JIANG Wei,ZHENG Zu-xiu.The algebraic criteria for the all-delay stability of two-dimensional degenerate differential systems with delay[J].Chinese Quarterly Journal of Mathematics,1998,13 (1):87-93.
[16] JIANG Wei,ZHENG Zu-xiu.The general solution of degenerate diff erence systems with delay[J]. Journal of Mathematical Study,1998,31(1):44-50.(in Chinese)
[17] Yip E L,Sincovec R F.Solvability,controllability and observability of continuous descriptor systems[J].IEEE Trans Automat Control,1981,26(3):702-706.
[18] ZHANG Guo-san,XIE Xu-kai.The DR-controllability of singular dispersed control system[J]. Control Theory and Applications,1995,12(6):704-711.(in Chinese)
[19] TANG Wan-sheng,LI Guang-quan.The criterion for controllability and observability of singular systems[J].Acta Automatica Sinica,1995,21(1):63-66.(in Chinese)
[20] JIANG Wei,WANG Zhi-cheng.The controllability of singular control systems[J].Journal of Hunan University,1999,26(4):6-9.(in Chinese)
[21] JIANG Wei,SONG Wei-zhong.Controllability of singular systems with control delay[J].Automatica,2001,37(11):1873-1877.

CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS

CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS

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