分段线性系统的李雅普诺夫函数：从不动点到极限环
Lyapunov Functions in Piecewise Linear Systems: From Fixed Point to Limit Cycle
摘要：
本文给出了一类具有极限环的分段线性系统构造李雅普诺夫函数的第一个例子。构造方法有助于通过新颖的几何手段分析和控制复杂的振荡系统。特别注意强调以前没有解决的问题：施加一致的边界条件的李雅普诺夫函数在每个线性区域。通过成功地解决这个问题，作者构造了连续的李雅普诺夫函数在整个状态空间。进一步证明了所构造的李雅普诺夫函数解释了导致极限环振荡出现的不同分岔。
英文摘要：
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means. Special attention is stressed upon a problem not formerly solved: to impose consistent boundary conditions on the Lyapunov function in each linear region. By successfully solving the problem, the authors construct continuous Lyapunov functions in the whole state space. It is further demonstrated that the Lyapunov functions constructed explain for the different bifurcations leading to the emergence of limit cycle oscillation.
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