The novel concepts and definitions of derivativeand bracket for nonlinear differential algebraic system (NDAS)are introduced, and some related revised results that are similarto the classic differential geometric theory are given. The normalforms of NDAS model are obtained by multi-input multi-output(MIMO) feedback linearization technique. The control expressionsderived are based on the linear system theory and the requirementsof tracking targets when the relative degree of the systemis less than the dimension of the system and the special designatedconditions are satisfied. The parametric adaptive controller is obtainedfor the multimachine power systems with nonlinear loadsand undetermined or unknown parameters by the Lyapunov stabilitytheory and method.

This paper gives the definition of Lie rotated vector fields in the plane andthe conditions of movement of singular points on Lie rotated vector fields with variableparameters.

Based on the definition of Lie rotated vector fields in the plane, this paper givesthe property of homoclinic orbit as parameter is changed and the singular points are fixedon Lie rotated vector fields. It gives the conditions of yielding limit cycles as well.

研究了连续时间混沌系统的参数自适应控制，提出了关于多重参数混沌非线性系统的参数自适应控制的新方法。考虑系统参数是线性形式的自适应控制，利用Lyapuno v 方法证明了参数控制方程是全局渐近稳定的。研究结果表明该控制方法是分析混沌参数自适应控制的一个十分有效的方法。

首次提出了用于控制微分代数系统的反馈线性化技术理论和方法，类似于经典的微分几何理论中的定义和定理，给出关于微分代数系统的M 导数、M 括号等一些新的定义，并给出了有关微分代数系统控制的一系列新结果，进一步拓广了非线性系统几何理论的应用范围。考虑到大多数电力系统模型都是采用微分代数模型，而且电力系统的负荷往往是电压和频率的非线性表达式，另外在实际工程中也常常遇到求非线性微分代数方程的最优控制解，引入微分代数系统的M 导数、M 括号等定义可较好地解决这类控制问题。利用控制微分代数系统的反馈线性化技术，能很好地应用于具有非线性负荷的电力系统非线性励磁控制的设计，使微分几何方法在电力系统控制研究中得到更广泛的应用。