非线性广义系统Lyapunov稳定性和输入—状态稳定性的关系

Relations between Lyapunov stability and ISS of nonlinear descriptor systems

研究非线性广义系统Lyapunov稳定性和输入—状态稳定性之间的关系问题.借助比较函数分析系统的Lyapunov稳定性,得到系统输入—状态稳定蕴涵系统全局渐近稳定.用反例说明对于一般的非线性广义系统,系统全局渐近稳定不能保证系统输入—状态稳定.

The problem of relations between Lyapunov stability and input-to-state stability （ISS） of nonlinear descriptor systems is discussed. Firstly, comparison functions are employed to analyse the Lyapunov stability of nonlinear descriptor systems. Then we derived the result that input-to-state stable implies global asymptotic stability for nonlinear descriptor systems. Conversely, for a general nonlinear descriptor system, global asymptotic stability does not guarantee input-to-state stable.