I. Introduction
Switched systems consist of several subsystems and a switching law specifying the active subsystems at each time instant [1], which are a particular class of hybrid systems. Switched systems have been the focus of many researchers for many years [2]–[7] due to a wide range of applications in engineering, including electrical circuits, mode-transitions, complex systems, and heterogeneous computation devices. In practice, most actuators for switched systems have saturation nonlinearity since the capability of any physical actuator is limited. If its adverse effect is neglected, actuator saturation will not only result in performance degradation of the closed-loop system but also can be the source of instability. For this reason, considerable attention has been paid to switched systems with actuators saturation [8]–[12]. Most work in [8]–[12] focuses on stabilization of switched systems with saturating actuators, however, which do not consider optimal control problem. From an application perspective, besides stabilization, performance is also crucial for switched systems with saturating actuators, which motivates our present research.