Optimal control approach to stability criteria on Hill's equations  

作　　者：ZU Jian LI Yong 

机构地区：[1]School of Mathematics and Statistics & Center for Mathematics and Interdisciplinary Sciences, North-east Normal University [2]Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University [3]College of Mathematics, Jilin University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2018年第3期253-273,共21页高校应用数学学报（英文版）（B辑）

基　　金：supported by NSFC(11401089,11671071);the Scientific Technological Project of Jilin Province’s Education Department in Thirteenth Five-Year(JJKH20170535KJ);supported by NSFC(11571065);the National Basic Research Program of China(2013CB834102)

摘　　要：This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill's equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov's criterion, Neǐgauz and Lidskiǐ's criterion. Secondly, we present stability criteria on Hill's equations with sign-changing potential in which Brog's criterion and Krein's criterion are included.

关 键 词：stability criteria optimal control method Hill's equation Lyapunov inequality 

分 类 号：O1[理学—数学]