Stability of a class of linear switching systems with applications to two consensus problems

2011 ◽  
Author(s):  
Youfeng Su ◽  
Jie Huang
Keyword(s):  
Switching Systems ◽  
Linear Switching Systems

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

Chaotification of a Class of Linear Switching Systems by Hybrid Driven Methods

2014 ◽  
Vol 24 (03) ◽  
pp. 1450033 ◽  
Author(s):  
Yuping Zhang ◽  
Xinzhi Liu ◽  
Hong Zhu ◽  
Yong Zeng
Keyword(s):  
Lyapunov Exponents ◽  
Continuous Time ◽  
Autonomous Systems ◽  
Phase Portraits ◽  
Computational Formula ◽  
Switching Systems ◽  
Time Switching ◽  
Switching Rule ◽  
Lyapunov Spectra ◽  
Linear Switching Systems

This paper investigates a class of linear continuous-time switching systems and proposes a new approach to generate chaos by designing a hybrid switching rule. First, a computational formula for Lyapunov exponents is derived by extending the definition of Lyapunov exponent for continuous-time autonomous systems to that of a class of linear continuous-time switching systems. Then, a novel switching rule is proposed to gain global boundedness property as well as the required placement of Lyapunov exponents for chaos. A numerical example is given to illustrate the chaotic dynamic behavior of the generated system. The Lyapunov dimension of the system in the example is calculated and the corresponding bifurcation diagram and Lyapunov spectra are sketched, which, together with other phase portraits, clearly verify the validity of the main result.

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