Average dwell time approach to ℒ 2 –ℒ ∞ control of switched delay systems via dynamic output feedback

This study is concerned with the ℒ2–ℒ∞ control problem for continuous-time switched systems with time-varying delay. A dynamic output feedback (DOF) controller is designed, which is assumed to be switching with the same switching signal as in the original system. By using an average dwell time approach and the piecewise Lyapunov function technique, a delay-dependent sufficient condition is proposed to guarantee the exponential stability and a weighted ℒ2–ℒ∞ performance for the closed-loop system with the decay estimate explicitly given. The corresponding solvability condition for a desired DOF controller is established, and an explicit parametrisation of all desired DOF controllers is also given. Finally, a numerical example is given to illustrate the effectiveness of the proposed theories.