Asymptotic Stability With Guaranteed Safety for Switched Nonlinear Systems: A Multiple Barrier Functions Method

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.