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$ 251 | 廣義膨脹和齊性--利用齊性構造齊次系統的李雅普諾夫函數和控制律(英文)
作者：（土）S.埃姆雷·圖納 出版社：哈爾濱工業大學出版社 出版日期：2021-06-01 語言：簡體中文 規格：平裝 / 125頁 / 13 x 19 x 1 cm / 普通級/ 1-1  博客來 - 數學
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圖書名稱：廣義膨脹和齊性--利用齊性構造齊次系統的李雅普諾夫函數和控制律(英文)
內容簡介
本書的目的是證明，如果考慮廣義擴張（它是一類群作用）並定義關於它們的齊次性，那麼齊次系統類可以變得非常一般。結果表明，解的唯一性（在時間的兩個方向上）確實是一個系統對某種廣義膨脹齊次的充分條件。本書研究了齊性與單調性的關係，證明了如果一個系統對某個V（正函數）是單調的，則存在一個廣義擴張，且系統和V都是齊次的。本書的另一個結果是在齊次條件下局部單調性與全域單調性的等價性。本書包括引言、離散時間的均勻性、齊次線性系統、連續時間的均勻性和切換均勻系統。
目錄
1 Introduction
1．1 Related work
1．2 Outline of the results
1．3 Notation and terminology
2 Homogeneity in Discrete Time
2．1 Generalized dilations and homogeneity
2．2 Examples of gilations
2．3 Homogeneous systems and optimization
2．4 Numerical calculations
2．5 A numerical example： discretized cubic integrator
2．6 Summary
2．7 Notes and references
3 Regulating a class of homogeneous systems
3．1 Regulation in continuous time
3．1．1 On robustness
3．2 Chained systems and systems in power form
3．2．1 Simulations
3．3 Summary
3．4 Notes and references
4 Homogeneity in continuous time
4．1 A condition on the righth and side
4．2 Homogeneity and uniqueness of solutions
4．3 Homogeneity and monotonicity
4．4 Implications when correlator is state independent
4．5 Summary
5 Switched homogeneous systems
5．1 Constructing a feedback
5．1．1 On robustness
5．1．2 Linear systems and convexity
5．2 A converse Lyapunov result
5．3 A numerical example
5．4 Summary
5．5 Notes and references
6 Conclusion
Bibliography
A On convergence of （2．19）
編輯手記
1．1 Related work
1．2 Outline of the results
1．3 Notation and terminology
2 Homogeneity in Discrete Time
2．1 Generalized dilations and homogeneity
2．2 Examples of gilations
2．3 Homogeneous systems and optimization
2．4 Numerical calculations
2．5 A numerical example： discretized cubic integrator
2．6 Summary
2．7 Notes and references
3 Regulating a class of homogeneous systems
3．1 Regulation in continuous time
3．1．1 On robustness
3．2 Chained systems and systems in power form
3．2．1 Simulations
3．3 Summary
3．4 Notes and references
4 Homogeneity in continuous time
4．1 A condition on the righth and side
4．2 Homogeneity and uniqueness of solutions
4．3 Homogeneity and monotonicity
4．4 Implications when correlator is state independent
4．5 Summary
5 Switched homogeneous systems
5．1 Constructing a feedback
5．1．1 On robustness
5．1．2 Linear systems and convexity
5．2 A converse Lyapunov result
5．3 A numerical example
5．4 Summary
5．5 Notes and references
6 Conclusion
Bibliography
A On convergence of （2．19）
編輯手記
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