Asymptotic Stability With Guaranteed Safety for Switched Nonlinear Systems: A Multiple Barrier Functions Method
本文提出一组条件，通过状态依赖切换律实现切换非线性系统的渐近稳定性并保证安全，不要求各子系统稳定，融合多障碍函数与多李雅普诺夫函数进行分析，并设计切换律避免芝诺现象。
In this article, a collection of conditions to achieve asymptotic stability of switched nonlinear systems with guaranteed safety via a state-dependent switching law are provided, where the asymptotic stability of individual subsystem is not assumed. Multiple barrier functions and multiple Lyapunov functions (MLFs) are merged as a tool for analyzing the asymptotic stability with guaranteed safety control problem of switched nonlinear systems. Meanwhile, the state-dependent switching law is designed to refrain zeno phenomenon. Moreover, bilinear sum of squares methodologies are employed to construct corresponding MLFs for switched nonlinear systems. Finally, three simulation examples are introduced to prove the effectiveness of the provided method.