State estimation for delayed switched positive systems: delayed radius approach

In this paper, an interval estimation scheme is developed for delayed switched positive systems (DSPS) with mode-dependent average dwell time switching. A lossless zonotopic estimation approach is proposed for the delayed intersection zonotope with the positive generator matrix. First, considering the existence of asynchronism between the system mode and the correction matrix mode, the mismatched intersection zonotope is constructed for DSPS to verify the consistency between the system model and outputs. Then, by utilizing the introduced radius definitions, the ℓ_∞ performance is addressed to optimize the size of delayed intersection zonotopes. Subsequently, we present a joint-design approach of switching signals and the mode-dependent correction matrix by constructing positive generator matrix-based delayed radius functions. Furthermore, guaranteed nonnegative state bounds are derived for the considered DSPS based on the proposed lossless zonotopic estimation criteria. Finally, detailed simulations are conducted to validate the feasibility and superiority of the developed methods.