Introduction

In order to do whatever we want with a dynamic system under control input, the dynamic system has to be controllable. Controllability plays a crucial role in many control problems, such as in complex networks [87], multi-fingered hands [9], spacecraft systems [70], dynamic power models [43], and so on. Note that nonlinear features are found in all practical systems almost. One of the nonlinear features in feedback control systems is saturation. Physical saturation is a key of control systems which are applicable to various aspects of engineering and science virtually [121, 153]. Saturation systems mainly include the following aspects: actuator saturation [81], state saturation [95], output saturation [194], multiple variable saturation [99], and so on. One of the most common saturation phenomenons is actuator saturation which has received much attention; please refer to [207, 209] and the references therein. A closed-loop system with actuator saturation is shown in Fig. 1.1.