On Asymptotic Stability of Discrete-Time Hybrid Systems

In this brief, we consider the asymptotic stability problem of a novel class of discrete-time hybrid systems. First, we introduce the so-called system in detail, which consists of discrete-time continuous-valued and Boolean dynamics. Second, we give the algebraic form of the systems by using the Khatri-Rao product and semi-tensor product (i.e., Cheng product). Third, we propose the concept of asymptotic stability for the hybrid systems. Further, based on Lyapunov functions, a necessary and sufficient condition is derived for testing asymptotic stability. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.