Non-Weighted <inline-formula> <tex-math notation="LaTeX">$L_2$ </tex-math></inline-formula>-Gain Control for Asynchronously Switched Linear Systems With Detectable Switching Instants and Ranged Mode-Identifying Time

Abstract

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.

Keywords

• Clock-dependent Lyapunov function
• L₂-gain%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> non-weighted <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">L</italic>₂-gain
• asynchronous control
• switched systems
• sum of square program