NDLI: New alternative convex conditions on exponential stability and stabilisation of switched positive linear systems with dwell time

Content Provider	IET Digital Library
Author	Li, Yang Zhang, Hongbin Xiang, Weiming
Abstract	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.
Starting Page	620
Ending Page	631
Page Count	12
ISSN	17518644
Volume Number	13
e-ISSN	17518652
Issue Number	Issue 5, Mar (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/13/5
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2018.5271
Journal	IET Control Theory & Applications
Publisher Date	2019-01-18
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Asymptotic Stability Continuous Time System Control System Analysis Discrete Control System Discrete Time System Dwell Time Stability Exponential Stability Infinite-dimensional Linear Programming Linear Programming Linear System Lyapunov Method Matrix Algebra Minimum Dwell Time New Alternative Convex Condition Nonconvex Condition Optimisation Technique Piecewise Linear Technique Stabilisation Problem Stability Stability Condition Stability in Control Theory Switched Positive Linear System Synthesis Method Time Varying System Transpose Condition
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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