非线性系统在乘积空间中的实用稳定性：直接方法

A Direct Approach to Practical Stability of Nonlinear Systems on Product Spaces

中文关键词  非线性系统  乘积空间  实用稳定性  向量直接方法  单调函数类

英文关键词  nonlinear system  practical stability  product spaces  vector direct method  monotonic function class

中文摘要

      本文研究非线性系统在乘积空间中的实用稳定性．利用向量辅助函数和适当的单调函数类，提出一种以微分比较原理和基本的单调性准则为基础的直接方法．它将问题归结为一组微分或积分（特殊地，代数）不等式条件，可以直接根据系统方程进行检验而无须引入并求解任何形式的比较系统，便于实际应用．文中给出了示例．

英文摘要

      This paper deals with the problem of practical stability of nonlinear systems on product spaces. Based on differential comparison principle and the basic monotonicity condition，a vector direct method is proposed in terms of vector auxiliary functions and proper class of monotonic functions. This method reduces the problem to verifying a set of differential or integral (specially，algebric) inequalities directly according to equations of the system under consideration，without requiring knowledge of solutions of any so-called "comparison systems" as that in many previous works. An illustrative example is worked out to demonstrate the availability of the presently proposed method.