大系统理论中的辅助方程组
The Auxiliary Simultaneous Equations in the Theory of Large Scale Systems
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摘要: 大系统理论中的辅助方程组在该理论中占有十分重要的地位.本文利用分块矩阵运算等 工具给出了辅助方程组系数矩阵的表达式,根据子系统的李雅普诺夫函数和原系统的系数矩 阵可以直接写出辅助方程组.利用本文的辅助方程组可以扩大参数的稳定性区域,得到比文 献[1-4]更好的结果.同时,研究了这一方法的推广和应用.Abstract: The auxiliary simultaneous equations in the theory of large scale systems play an important role in this theory. The coefficient matrix expressions of the auxiliary simultaneous equations that can be written out directly following the Lyapunov function of subsystems and the coefficient matrix of the original system with the operation of block matrix are given in this paper. The stability region of parameters can be enlarged using the auxiliary simultaneous equations obtained, and some results better than those in [1]--[4] are also obtained. Some extensions of this method and its applications have also been studied.
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