Finite-time stability and stabilization of discrete-time hybrid systems

This paper is concerned with the finite-time stability and stabilization problems for a class of hybrid systems, which consists of discrete-time continuous-valued and Boolean dynamics. First, we introduce the so-called systems briefly and give the algebraic form of the systems via Khatri–Rao product and semi-tensor product (STP, i.e., Cheng product). Next, we originally propose the concept of finite-time stability (FTS) for the hybrid systems. Furthermore, some criteria of FTS for the hybrid systems are provided. Via a lemma we present, the computational complexity of the condition on FTS for the logical part could be reduced to $O\left(1\right)$. Based on these obtained results, two classes of controllers, state feedback controllers and logical controllers, are designed. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results.