Asynchronous positive filter design for switched positive systems with overlapped detection delay

Abstract

In this study, the asynchronous positive filtering problem for a class of switched positive system with detection delay is investigated. The switched sequence satisfies modal‐dwell‐time (MDT) condition and the detection delay is both time‐varying and allowed to be overlapped with each other. A new linear copositive Lyapunov function, which is time‐dependent, mode‐dependent and MDT‐dependent, is constructed and the stability of the underlying filtering error system is established. Based on the established stability result, conditions guaranteeing the stability of the corresponding filtering error system are further derived. The allowable total running time of the unmatched sub‐filters is presented to be upper bounded by a linear combination of those running on matched sub‐filters. An asynchronous positive filter with disturbance suppression performance for the underlying switched positive system with overlapped detection delay is designed by solving a linear programming problem. The effectiveness of the proposed filter is illustrated by a numerical example.