Stability, L_1-gain analysis and asynchronous L_1-gain control of uncertain discrete-time switched positive linear systems with dwell time

摘要

In this paper, the stability, L-1-gain analysis and asynchronous L-1-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L-1-gain analysis and asynchronous L-1-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L-1-gain analysis and asynchronous L-1-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L-1-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results. (C) 2018 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.