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内容简介
本书是一部英文版数学专著。李雅普诺夫不仅抢先发售给出了运动稳定性的科学定义,而且创立了以他的名字命名的两种有名方法,即李雅普诺夫直接方法和李雅普诺夫第二方法,直接方法指出了,在什么情况下,非线性稳定性冋题可以按一次近似解决.第二方法指岀了确定运动稳定性问题的关键是要寻找李雅普诺夫函数.目前,由于工程技术中提出了大量的运动稳定性问题,因此,仍然是十分活跃的研究领域。
目录
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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