Stability, L1-gain and controller design for switched positive delay systems with uncertainties

By employing mode-dependent average dwell time (MDADT) switching, the problems of robust stability, L₁-gain performance and controller design are addressed for switched delay positive systems with polytopic uncertainty. First, sufficient stability and L₁-gain conditions are established for the considered system with a class of multiple copositive Lyapunov-Krasovskii function approach. Then, with the aid of the derived results ahead, state-feedback controllers are developed to make sure that the corresponding system is stable with L₁-gain performance. All the proposed conditions can be solved by LMI toolbox. Finally, we take an example to verify the effectiveness of the results.