On Decentralized Stabilization of Linear Large Scale Systems With Symmetric Circulant Structure
-
摘要: 研究一类具有对称循环结构的连续和离散线性大系统的分散镇定特征，充分利用对称循环的特点，建立了判断这类系统可分散镇定的充分条件．在连续情形下，通过引进耦合结构模这一概念，揭示了这类系统分散镇定的重要特征，这就是当整个系统的耦合结构模给定之后，系统的分散镇定特性可以完全由各孤立子系统的结构所决定．这表明在这类系统的实际设计中，不管系统内中各子系统之间的耦合结构多么复杂，只要按一定的条件适当设计或修正各孤立子系统的结构参数，就能使所设计的大系统具有分散镇定特征，并提供了相应的分散镇定算法．对离散情形也进行了讨论，结果表明，连续系统与离散系统的分散镇定特征有着很大的差异．Abstract: The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied. A few sufficient conditions on decentralized stabilization of such systems were proposed. For the continuous systems, by introducing a concept called the magnitude of interconnected structure, a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given. So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem, no matter how complicated the interconnected structure of the overall system is. A algorithm for obtaining decentralized state feedback to stabilize the overall system is given. The discrete systems were also discussed. The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.
-
[1] Geromel J C,Yamakami A.Stabilization of continuous and discrete linear systems subjected to control structure constraints[J].Internat J Control,1982,36(3):429—444. doi: 10.1080/00207178208932906 [2] Lee T N,Radovic U L.Decentralized stabilization of linear continuous and discrete-time systems with delays in interconnections[J].IEEE Trans Automat Control,1988,33(3):757—761. doi: 10.1109/9.1293 [3] Ikeda M,Siljak D D,Yasuda K.Optimality of decentralized control for large-scale systems[J].Automatica—J IFAC,1983,19(3):309—316. doi: 10.1016/0005-1098(83)90109-7 [4] 金朝永.Vandermonde矩阵的逆模与大系统的分散镇定性[J].高校应用数学学报，A辑，1997，12(2)：219—228. [5] 金朝永.一类含参数的分块对称矩阵的正定性及应用[J].高校应用数学学报，A辑，2001，16(1)：107—113. [6] JIN Chao-yong.Decentralized stabilization of a class of interconnected systems[J].Appl Math J Chinese Univ，Ser B,2001,12(3):330—338. [7] Brockett R W,Willems J L.Discretezed partial differential equations:examples on control systems defined on modules[J].Automatica,1974,10(4):507—515. doi: 10.1016/0005-1098(74)90051-X [8] Hovd M,Skogestad S.Control of symmetrically interconnected plants[J].Automatica,1994,30(6):957—973. doi: 10.1016/0005-1098(94)90190-2 [9] 黄守东，张嗣瀛.具有对称循环结构的大系统Ricatti方程的求解[J].控制理论与应用，1998，15(1)：75—81. -
计量
- 文章访问数: 2368
- HTML全文浏览量: 67
- PDF下载量: 639
- 被引次数: 0
下载:
渝公网安备50010802005915号