ℋ ∞ control for asynchronously switched linear parameter‐varying systems with mode‐dependent average dwell time

This study is concerned with the stability, l 2 ‐gain analysis and ℋ ∞ control for a class of discrete‐time switched linear parameter‐varying systems with both mode‐dependent average dwell time (MDADT) and asynchronous switching, where ‘asynchronous’ means the switching of controllers has a lag to the switching of system modes. The l 2 ‐gain for general switched systems with MDADT in non‐linear setting is firstly derived. Based on the obtained results, the problem of asynchronous ℋ ∞ control for the studied systems is formulated under the framework of MDADT switching logic, and the conditions for the existence of admissible asynchronous ℋ ∞ controllers are deduced in the form of parameterised linear matrix inequalities. A numerical example is provided to verify the effectiveness of the acquired results.