Positive Definiteness of a Class of Analytic Functions  

作　　者：苗原 李春文 张平 

出　　处：《Tsinghua Science and Technology》1997年第3期19-22,共4页清华大学学报（自然科学版（英文版）

摘　　要：Some singular characteristics of analytic functions with positive definiteness are considered. To avoid these singular cases, the finite truncate condition is proposed. When the finite truncate condition is satisfied, the positive definiteness of an analytic function can be judged by the partial sum of its Taylor series, i e , by a polynomial. This discussion will be useful in the construction of Lyapunov functions for nonlinear systems. Some singular characteristics of analytic functions with positive definiteness are considered. To avoid these singular cases, the finite truncate condition is proposed. When the finite truncate condition is satisfied, the positive definiteness of an analytic function can be judged by the partial sum of its Taylor series, i e , by a polynomial. This discussion will be useful in the construction of Lyapunov functions for nonlinear systems.

关 键 词：positive definte finite truncate condition POLYNOMIAL 

分 类 号：O156.4[理学—数学]