BMI Approach to the Interconnected Stability and Cooperative Control of Linear Systems
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摘要: 本文研究了线性大系统的关联稳定与协调控制问题. 基于双线性矩阵不等式, 给出了两个子系统关联稳定与协调镇定的充分与必要条件. 结论表明, 即使子系统不稳定, 组成的大系统也易能被协调镇定, 而不需要假定子系统的稳定. 其次, 协调控制器的设计问题转化为 BMI 约束下的优化问题, 为求解此问题, 提出了优化交替算法, 并给出了此算法收敛性的简单证明. 最后, 数值算例表明了优化算法的有效性.Abstract: This paper studies the interconnected stability and cooperative control of large-scale linear systems. Using the technique of the bilinear matrix inequality (BMI), the necessary and sufficient conditions are given for interconnected stability and cooperative stabilization of two subsystems. It is shown that the systems can be cooperatively stabilized even if the subsystems are not stable. It is not necessary for us to presume the stability of the subsystems. Furthermore, the problems of designing interconnected and cooperative controllers are converted into the optimization problems using BMI constraints. To solve these problems, certain optimal alternate algorithms are proposed, and the proof for the convergence of the algorithms is presented. Finally, several examples are given to illustrate the optimization results.
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