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.

scholarly journals CHAOTIFYING CONTINUOUS-TIME NONLINEAR AUTONOMOUS SYSTEMS

2012 ◽  
Vol 22 (09) ◽  
pp. 1250232 ◽  
Author(s):  
SIMIN YU ◽  
GUANRONG CHEN
Keyword(s):  
Linear Systems ◽  
Lyapunov Exponents ◽  
Continuous Time ◽  
Autonomous Systems ◽  
Nonlinear Function ◽  
Positive Zero ◽  
State Variables ◽  
Nonlinear Feedback ◽  
Special Cases ◽  
Time Autonomous

Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e. being globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible and unified chaotification method for designing a general chaotic continuous-time autonomous nonlinear system. For a system consisting of a linear and a nonlinear subsystems, chaotification is achieved using separation of state variables, which decomposes the system into two open-loop subsystems interacting through mutual feedback resulting in an overall closed-loop nonlinear feedback system. Under the condition that the nonlinear feedback control output is uniformly bounded where the nonlinear function is of bounded-input/bounded-output, it is proved that the resulting system is chaotic in the sense of being globally bounded with a required placement of Lyapunov exponents. Several numerical examples are given to verify the effectiveness of the theoretical design. Since linear systems are special cases of nonlinear systems, the new method is also applicable to linear systems in general.

Constructing Chaotic Systems from a Class of Switching Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1850032 ◽  
Author(s):  
Yuping Zhang ◽  
Xinzhi Liu ◽  
Huaiyue Zhang ◽  
Chunhua Jia
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Switching Systems ◽  
Heteroclinic Loop ◽  
Time Switching ◽  
Loop Design ◽  
Implementation Scheme ◽  
Shilnikov Criterion

This paper aims to develop an approach for constructing chaotic systems from a class of linear continuous-time switching systems. First, the Shilnikov criterion is analyzed and extended to the switching systems. Then some kinds of “swing planes” are provided via a heteroclinic loop design, which act as switching planes to chaotify the systems. Furthermore, a numerical example is presented to validate the proposed principle and implementation scheme. The theoretical analysis and numerical simulation have demonstrated the feasibility and effectiveness of the developed techniques.

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.

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