I. Introduction
As one kind of hybrid systems, a switched nonlinear system consists of a family of subsystems and a switching rule that orchestrates the switching among those subsystems. In recent years, the control issues of switched systems have been paid considerable attention due to their wide applications in practice engineering, such as the control of mechanical systems, the automotive industry, aircraft and air traffic control, and so on [1]–[3]. It was provided that under arbitrary switching conditions, a switching system is asymptotically stable if a common Lyapunov function exists for each subsystem [4]. By the common Lyapunov function approach, some remarkable results have been presented for switched linear systems in [5] and [6]. Note that nonlinearities widely exist in practice systems. Many scholars have recently paid attention to switched nonlinear systems under arbitrary switching [7]–[10]. In [11], multiple Lyapunov functions approach was used to deal with disturbance rejection problem of switched nonlinear systems. In [12], adaptive tracking control was addressed for switched nonlinear systems with uncertainties. The proposed controllers via state feedback guaranteed a good tracking performance. The work in [13] dealt with the global stabilization of stochastic switched nonlinear systems under arbitrary switchings.