Robust H∞ Reliable Control of Uncertain Switched Nonlinear Systems with Time-varying Delay

Abstract

Switched systems are a class of hybrid system consisting of subsystems and a switching law, which define a specific subsystem being activated during a certain interval of time. Many real-world processes and systems can be modeled as switched systems, such as the automobile direction-reverse systems, computer disk systems, multiple work points control systems of airplane and so on. Therefore, the switched systems have the wide project background and can be widely applied in many domains (Wang, W. & Brockett, R. W., 1997; Tomlin, C. et al., 1998; Varaiya, P., 1993). Besides switching properties, when modeling a engineering system, system uncertainties that occur as a result of using approximate system model for simplicity, data errors for evaluation, changes in environment conditions, etc, also exit naturally in control systems. Therefore, both of switching and uncertainties should be integrated into system model. Recently, study of switched systems mainly focuses on stability and stabilization (Sun, Z. D. & Ge, S. S., 2005; Song, Y. et al., 2008; Zhang, Y. et al., 2007). Based on linear matrix inequality technology, the problem of robust control for the system is investigated in the literature (Pettersson, S. & Lennartson, B., 2002). In order to guarantee H∞ performance of the system, the robust H∞ control is studied using linear matrix inequality method in the literature (Sun, W. A. & Zhao, J., 2005). In many engineering systems, the actuators may be subjected to faults in special environment due to the decline in the component quality or the breakage of working condition which always leads to undesirable performance, even makes system out of control. Therefore, it is of interest to design a control system which can tolerate faults of actuators. In addition, many engineering systems always involve time delay phenomenon, for instance, long-distance transportation systems, hydraulic pressure systems, network control systems and so on. Time delay is frequently a source of instability of feedback systems. Owing to all of these, we shouldn’t neglect the influence of time delay and probable actuators faults when designing a practical control system. Up to now, research activities of this field for switched system have been of great interest. Stability analysis of a class of linear switching systems with time delay is presented in the literature (Kim, S. et al., 2006). Robust H∞ control for discrete switched systems with time-varying delay is discussed