层次差异消除法镇定一类非线性组合大系统

Eliminating Differences Between Layers to Stabilize Nonlinear Similar Interconnected System with Uncertainties

引进相似变换,以减少或消除子系统间的层次差异,提出了一层次差异消除准则,进而运用比较原理和矩阵指数性质,建立了非线性关联子系统矩阵特征值与系统稳定性之间的关系,将一类具有非线性系统的镇定问题转换成经典的特征值配置问题.本文仅需假定系统的非线性(可能含不确定性)成分具范数界,不必要求其范数满足匹配条件.数值例子表明所给出的方法的有效性,并与相关成果进行了比较.

A similar method to eliminate or remove the differences existing in layers of the systems is introduced.A removestandard is developed,which is shown with constrain condition.The relationship between the asymptotic stability of the nonlinear connected system and its eigenvalues is investigated by applying property of Mmatrix based on analysis of the structure of differential equations,which is used to convert the controller design to the classical pole placement.The only assumption is that the nonlinear components possibly including uncertainties are bounded with universal norm,no restrictive as to the polymatrix structure or matched condition is need.An algebraic procedure is provided for controller that is required to satisfy performances.Comparisons with previous results are made and the illustrative example shows that our method is valid.