非线性控制系统的Runge-Kutta方法的输入状态稳定  

Input-to-State Stability of Runge-Kutta Method of Nonlinear Control System

作　　者：范振成 FAN Zhencheng(College of Computer and Data Science,Minjiang University,Fuzhou,Fujian 350108,China)

机构地区：[1]闽江学院计算机与大数据学院,福建福州350108

出　　处：《闽江学院学报》2024年第2期1-6,共6页Journal of Minjiang University

基　　金：福建省自然科学基金项目(2021J011031)。

摘　　要：研究在什么条件下Runge-Kutta方法能够保持非线性控制系统的输入状态稳定。给出了Runge-Kutta方法生成的近似解保持控制系统真解的输入状态稳定的充分条件,特别证明了在一些常规条件下,所有Gauss-Legendre,Radau IA,Radau IIA,Lobatto IIIC型方法生成的近似解能够保持控制系统真解的输入状态稳定,这为实际应用中如何选择控制系统的数值方法问题奠定了理论基础。We investigate the conditions under which Runge-Kutta methods can preserve the input-to-state stability(ISS)of nonlinear control sysytems.We give some sufficient conditions under which the numerical solutions generated by Runge-Kutta methods can preserve the ISS of true solutions of nonlinear control systems,and especially prove the numerical solutions generated by all Gauss-Legendre,Radau IA,Radau IIA and Lobatto IIIC methods can preserve ISS of true solutions under some general conditions,which lay a theoretical foundation for choice of numerical methods of discretizing some control systems in practical application.

关 键 词：控制系统 RUNGE-KUTTA方法 输入状态稳定 

分 类 号：O241.8[理学—计算数学]