Finite-time Issue of Discrete-time Linear Switched Systems With Partial Finite-time Unstable Modes Based on an Inverse Weighted Switching Scheme

The work proposes a multiple convex Lyapunov function and an inverse weighted switching scheme to investigate the finite-time stability and finite-time boundedness for a class of discrete-time switched linear systems with partial finite-time unstable modes. A multiple convex Lyapunov function is put...

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Bibliographic Details
Published in:International journal of control, automation, and systems Vol. 22; no. 2; pp. 475 - 488
Main Authors: Zhan, Yunpeng, Wang, Ruihua, Fei, Shumin
Format: Journal Article
Language:English
Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.02.2024
Springer Nature B.V
제어·로봇·시스템학회
Subjects:
Circuits
Control
Controllability
Discrete time systems
Dwell time
Engineering
Liapunov functions
Linear systems
Matrices (mathematics)
Mechatronics
Regular Papers
Robotics
Subsystems
Switching
Systems stability
Tunnel diodes
제어계측공학
finite-time stability
Discrete-time linear switched systems
finite-time boundedness
inverse weighted switching scheme
multiple convex Lyapunov function
finite-time unstable modes
ISSN:1598-6446, 2005-4092
Online Access:Get full text
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Summary:The work proposes a multiple convex Lyapunov function and an inverse weighted switching scheme to investigate the finite-time stability and finite-time boundedness for a class of discrete-time switched linear systems with partial finite-time unstable modes. A multiple convex Lyapunov function is put forth by constructing a convex combination of positive definite matrices, which can relax the restricted conditions of the Lyapunov function and make it carry more decision variables than traditional Lyapunov function methods. Besides, the inverse weighted switching scheme is devised by summing the reciprocal of each dwell time with weighting coefficients, by which tighter dwell time bounds are ensured. On the basis of the new Lyapunov function and switching scheme, the finite-time control for a class of switched linear systems with partial finite-time unstable modes is addressed. Different from other researches that require all subsystems to be controllable, we only require the existence of one controllable subsystem. In the end, two numerical examples and a tunnel diode circuit example are provided to verify the effectiveness of the developed results.
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http://link.springer.com/article/10.1007/s12555-022-0498-5
ISSN:1598-6446
2005-4092
DOI:10.1007/s12555-022-0498-5