Stability and stabilization for discrete-time positive switched multiple equilibria systems on finite time intervals
LIU Zhi
ZHANG Xian-fu
WANG Yu-zhen
Abstract：The interference of the external environment or the development and changes of things will lead to the phenomenon of multiple equilibria in the switching events. Compared with the model of general switched systems, the model of multiple equilibria switched systems are better to describe these situations. This paper studies the stability and stabilization for discrete-time multiple equilibria positive switched systems (DT–MEPSSs) on finite time intervals. Firstly, the necessary and sufficient condition of positivity for the switched multiple equilibria systems is proposed. Secondly, the definition of finite time stability for the MEPSSs is given. Thirdly, by establishing a suitable Lyapunov function and managing the dwell time and the number of switching times, a sufficient condition of finite time stability for the DT-MEPSS with unstable subsystems is provided. Fourthly, the controller design for the non-autonomous MEPSS is presented. Finally, a simulation example is given to verify the correctness of the obtained results.
Keywords：positive switched linear systemsmultiple equilibriaunstable subsystemsfinite time stabilitystabilization
Publication Date：2017-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：8( 433-440 )