Asynchronous L1-gain control of uncertain switched positive linear systems with dwell time

In this paper, dwell time (DT) stability, L1-gain performance analysis and asynchronous L1-gain controller design problems of uncertain switched positive linear systems (SPLSs) are investigated. Via a time-scheduled multiple linear co-positive Lyapunov function (TSMLCLF) approach, convex sufficient conditions of DT stability and L1-gain performance of SPLSs with interval and polytopic uncertainties are presented. Furthermore, by utilizing the feature that the TSMLCLF keeps decreasing even if the controller is running asynchronously with the system, the asynchronous L1-gain controller design problem of SPLSs with interval and polytopic uncertainties is investigated. Convex sufficient conditions of the existence of time-varying asynchronous state-feedback controller which can ensure the closed-loop system's positivity, stability and L1-gain performance are established, and the controller gain matrices can be calculated instantaneously online. The obtained L1-gain in the paper is standard. All the results are presented in terms of linear programming. A practical example is provided to show the effectiveness of the results.