广义膨胀和齐性——利用齐性构造齐次系统的李雅普诺夫函数和控制律

本书的目的是证明，如果考虑广义扩张（它是一类群作用）并定义关于它们的齐次性，那么齐次系统类可以变得一般。结果表明，解的性（在时间的两个方向上）确实是一个系统对某种广义膨胀齐次的充分条件。本书研究了齐性与单调性的关系，证明了如果一个系统对某个V（正函数）是单调的，则存在一个广义扩张，且系统和V都是齐次的。本书的另一个结果是在齐次条件下局部单调性与全局单调性的等价性。本书包括引言、离散时间的均匀性、齐次线性系统、连续时间的均匀性和切换均匀系统。

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）
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