TY - JOUR
T1 - New alternative convex conditions on exponential stability and stabilisation of switched positive linear systems with dwell time
AU - Li, Yang
AU - Zhang, Hongbin
AU - Xiang, Weiming
N1 - Funding Information:
The authors thank the reviewers for their helpful comments and suggestions, which have helped improve the quality of the paper. The work was supported by the National Natural Science Foundation of China under grants 61374117 and 61603312.
Publisher Copyright:
© The Institution of Engineering and Technology 2019.
PY - 2019
Y1 - 2019
N2 - This study is concerned with dwell time stability and stabilisation problems of switched positive linear systems (SPLSs). The dwell time refers to minimum dwell time and constant dwell time. Several stability conditions for primal and transpose SPLSs with dwell time are presented, and the relation between these conditions is illustrated. Some of these conditions are given in terms of infinite-dimensional linear programming (LP), which cannot be solved directly. Then, by utilising the piecewise linear approach, new alternative convex conditions are formulated in terms of finite-dimensional LP. Compared to the existing literature, results with lower or at least the same conservatism can be obtained under the new conditions for the same discretised order. An algorithm is given to reduce the computational cost. Meanwhile, it is proved that there exists a relation between these convex and non-convex conditions if the discretised order is sufficiently large. By utilising the transpose conditions, alternative convex conditions on stabilisation of SPLSs with dwell time are also presented. The controller gain matrices can be computed by solving a set of LP directly. Finally, the correctness and superiority of the results are verified by numerical examples.
AB - This study is concerned with dwell time stability and stabilisation problems of switched positive linear systems (SPLSs). The dwell time refers to minimum dwell time and constant dwell time. Several stability conditions for primal and transpose SPLSs with dwell time are presented, and the relation between these conditions is illustrated. Some of these conditions are given in terms of infinite-dimensional linear programming (LP), which cannot be solved directly. Then, by utilising the piecewise linear approach, new alternative convex conditions are formulated in terms of finite-dimensional LP. Compared to the existing literature, results with lower or at least the same conservatism can be obtained under the new conditions for the same discretised order. An algorithm is given to reduce the computational cost. Meanwhile, it is proved that there exists a relation between these convex and non-convex conditions if the discretised order is sufficiently large. By utilising the transpose conditions, alternative convex conditions on stabilisation of SPLSs with dwell time are also presented. The controller gain matrices can be computed by solving a set of LP directly. Finally, the correctness and superiority of the results are verified by numerical examples.
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U2 - 10.1049/iet-cta.2018.5271
DO - 10.1049/iet-cta.2018.5271
M3 - Article
AN - SCOPUS:85064668015
SN - 1751-8644
VL - 13
SP - 620
EP - 631
JO - IET Control Theory and Applications
JF - IET Control Theory and Applications
IS - 5
ER -