论文标题
Max-Min Lyapunov的开关系统和相关差分包含功能
Max-Min Lyapunov Functions for Switched Systems and Related Differential Inclusions
论文作者
论文摘要
从一个有限的持续微分积极的确定功能开始，我们研究了通过Max-Min组合获得的功能是Lyapunov的函数，它为两种非线性动力学系统建立了稳定性：a）设置值的右手右侧右侧右侧右侧右侧的右手均包含了均由VECTER SORVITY和B）自动转换的convex hull and Scontions and B）切换。我们研究了这些最大值函数的定向衍生物的广义概念，并将其用于得出具有不同程度的保守主义的稳定条件，在数值上更加易于处理。所提出的构造还提供了非Convex lyapunov函数，这些功能可用于具有状态依赖性开关的系统，而该系统不接受凸Lyapunov函数。包括几个示例来说明结果。
Starting from a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations is a Lyapunov function, establishing stability for two kinds of nonlinear dynamical systems: a) Differential inclusions where the set-valued right-hand-side comprises the convex hull of a finite number of vector fields, and b) Autonomous switched systems with a state-dependent switching signal. We investigate generalized notions of directional derivatives for these max-min functions, and use them in deriving stability conditions with various degrees of conservatism, where more conservative conditions are numerically more tractable. The proposed constructions also provide nonconvex Lyapunov functions, which are shown to be useful for systems with state-dependent switching that do not admit a convex Lyapunov function. Several examples are included to illustrate the results.
