I. INTRODUCTION

II. SYSTEM DESCRIPTION AND PRELIMINARIES

III. MAIN RESULTS

IV. SIMULATION

V. CONCLUSION

ACKNOWLEDGMENT

REFERENCES

In this paper, the non-weighted L2-gain control problem is addressed for a class of asynchronously switched linear systems, where the asynchronous phenomenon is caused by the mode-identifying process. Unlike the literature concerned with asynchronously switched systems, we construct a new class of clock-dependent Lyapunov function (CDLF), which can be permitted or prohibited to increase when the modes of the controller and system are unmatched. Furthermore, a novel controller design strategy is introduced. The asynchronous and synchronous controllers are designed separately, and are both clock-dependent. By using the CDLF approach, a clock-dependent sufficient condition characterizing the non-weighted L2-gain performance is obtained for the asynchronously switched systems. The controller gains can be computed by solving a set of sum of square (SOS) program. At last, the advantages of the results are illustrated within two examples.

INTRODUCTION

In recent decades, switched systems have gotten a lot of attention in virtue of its practical and theoretical values. This class of systems consists of several continuous-time or discrete- subsystems with a switching signal driving them. The feature of switching widely exists in real-world systems, thereby many practical systems can be modeled by switched systems, such as chemical system [1], traffic system [2] and teleoperation robotic system [3]. In practice, a system possessing switching feature may be not stabilized by using any common control inputs, but can be stabilized by using switching control inputs. In other words, one needs to apply different control inputs to different subsystems. Therefore, the switching control problem for switched systems has been researched deeply in some literature, e.g., [3]–[۱۲]. Within most of the aforementioned work, it’s assumed that the mode of the controller is always consistent with the system’s. However, the controller may not switch synchronously with the system in real-world system. Since the mode-identifying process requires some time to complete, the modes of the controller and the system may be unmatched during this period of time. The system which contains unmatched controller is called asynchronously switched system. In the last decade, abundant results have been obtained for asynchronously switched systems with time-controlled switching signal, e.g., [13]–[۲۸].