Total Poisson Boundedness of Solutions of P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document}-Perturbed Complex Systems of Differential Equations

被引：0
作者：
K. S. Lapin
机构：
[1] Mordovian State Pedagogical Institute named after M.E. Evseviev,
来源：
Russian Mathematics | 2019年 / 63卷 / 10期
关键词：
-perturbed system; complex system; Lyapunov function; total Poisson boundedness of solutions;
D O I：
10.3103/S1066369X19100074
中图分类号：
学科分类号：
摘要：
We introduce the concepts of P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document}-perturbed system and, in particular, P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document}-perturbed complex system. Based on the method of Lyapunov functions, we obtain the sufficient condition of total Poisson boundedness of solutions to the P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document}-perturbed system with respect to any linear system with constant coefficients. Based on the method of vector Lyapunov functions and the above-stated condition, we obtain sufficient conditions of total Poisson boundedness of solutions to the P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document}-perturbed complex system and solutions to the P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document}-perturbed complex system with feedback loop.
引用
收藏
页码：55 / 65
页数：10
相关论文
共 9 条
[1]  
Yoshizawa T(1959)Liapunov’s Function and Boundedness of Solutions Funkcialaj Ekvacioj 2 95-142
[2]  
Bailey FN(1965)The Application of Lyapunov’s Second Method to Interconnected Systems SIAM J. Control (USA), ser. A. 3 443-462
[3]  
Lapin KS(2018)Uniform Boundedness in the Sense of Poisson of Solutions of Systems of Differential Equations and Lyapunov Vector Functions Differential equations 54 38-48
[4]  
Lapin KS(2018)Ultimate Boundedness in the Sense of Poisson of Solutions to Systems of Differential Equations and Lyapunov Functions Math. Notes 103 221-231
[5]  
Lapin KS(2018)Vector Lyapunov Functions and Ultimate Poisson Boundedness of Solutions of Systems of Differential Equations Math. Notes 104 63-73
[6]  
Lapin KS(2018)Poisson Total Boundedness of Solutions of Systems of Differential Equations and Lyapunov Vector Functions Math. Notes 104 253-262
[7]  
Lapin KS(2019)Higher Lyapunov Functions Derivatives and Total Poisson Boundedness of Solutions Russian Mathematics 63 17-24
[8]  
Piontkovskii AA(1968)Investigation of Certain Stability-theory Problems by the Vector Lyapunov Function Method Automat. Remote Control 10 1422-1429
[9]  
Rutkovskaya LD(undefined)undefined undefined undefined undefined-undefined
1