GENERATION AND CONTROL OF SPHERICAL AND CIRCULAR ATTRACTORS USING SWITCHING SCHEMES

2007 ◽  
Vol 17 (01) ◽  
pp. 243-253 ◽  
Author(s):  
QINGFEI CHEN ◽  
QIUHAI ZHONG ◽  
YIGUANG HONG ◽  
GUANRONG CHEN
Keyword(s):  
Nonlinear Systems ◽  
Switched Systems ◽  
Underlying Mechanism ◽  
Chaotic Attractors ◽  
Switched Nonlinear Systems ◽  
And Control

Construction of special (chaotic) attractors for various design demands has drawn much attention recently. This paper studies the generation of a family of spherical and circular quasi-periodic/chaotic attractors from simple switched nonlinear systems. Controllers are designed for manipulating the sizes or shapes of islands and bridges in such circular attractors. The underlying mechanism of generating these attractors from the switched systems is investigated.

scholarly journals On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Discrete Time ◽  
Switched Systems ◽  
Multiple Delays ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Arbitrary Switching ◽  
Aggregation Techniques ◽  
Robust Stability Analysis

This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.

scholarly journals On Finite-Time Stability of Switched Systems with Hybrid Homogeneous Degrees

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bin Zhang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Nonlinear Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Numerical Example

The finite-time stability is investigated for switched nonlinear systems. It is assumed that each subsystem possesses a positive homogeneous Lyapunov-like function. The derivative of the function is with hybrid homogenous degrees. Three substantially different situations are considered and different sufficient conditions are provided, respectively. The utility of our result is illustrated through the study of a numerical example.

scholarly journals Stability of switched systems with admissible switching signals

2021 ◽  
Author(s):  
Hui-Ting Wang ◽  
Yong He ◽  
Qing-Guo Wang ◽  
Chuan-Ke Zhang ◽  
Min Wu
Keyword(s):  
Nonlinear Systems ◽  
Stability Condition ◽  
Switched Systems ◽  
Dwell Time ◽  
Divergence Time ◽  
Average Dwell Time ◽  
Sufficient Condition ◽  
Switched Nonlinear Systems ◽  
Equal Compensation ◽  
Stability Results

Abstract In this paper, stability of switched systems is investigated for a class of switching signals which meet some admissibility conditions. Firstly, the admissible edge-dependent divergence time is defined in terms of admissible transition edges and it will vary with the compensation bounds. Then the admissible edge-dependent bounded maximum average dwell time (BMADT) is imposed on switching signals. As a result, a sufficient condition is obtained for globally uniformly exponential stability of switched nonlinear systems with such switching signals. Secondly, by setting the equal compensation bounds for the same reaching subsystems, the mode-dependent divergence time is defined, and then the mode-dependent BMADT is proposed. A stability condition under the mode-dependent BMADT is established. These stability results are then applied to switched linear systems. The numerical example is presented to show that the proposed techniques are less restrictive and more flexible in application, compared with the BMADT.

Input-to-state stability for impulsive switched nonlinear systems with unstable subsystems

2017 ◽  
Vol 40 (7) ◽  
pp. 2167-2177 ◽  
Author(s):  
Meng Zhang ◽  
Lijun Gao
Keyword(s):  
Nonlinear Systems ◽  
Lower Bound ◽  
Lyapunov Function ◽  
Upper Bound ◽  
Switched Systems ◽  
Impulsive Effects ◽  
Switched Nonlinear Systems ◽  
Unstable Subsystems ◽  
Interval Approach ◽  
Impulsive Switched Systems

In this article, the input-to-state stability is investigated for impulsive switched systems. By means of the Lyapunov function and the average impulsive switched interval approach, the input-to-state stability properties are derived under the condition that all subsystems are stable, all subsystems are unstable and some subsystems are unstable. It is shown that if the continuous subsystems all have input-to-state stability and though the impulsive effects are destabilizing, the system has input-to-state stability with respect to a lower bound of the average impulsive switched interval. Moreover, if all the subsystems do not have input-to-state stability, the impulsive effects can still successfully stabilize the system but for an upper bound of the average impulsive switched interval. However, it is unveiled that if some continuous subsystems are not input-to-state stability, the impulsive effects can successfully stabilize the system for a lower bound of the average impulsive switched interval under specific conditions. It is worth noting that we introduce multiple jumps in this paper. Finally, three examples are illustrated with their simulations to manifest the validity of the main results.

Uniform Stability of Discrete-Time Switched Nonlinear Systems

2014 ◽  
Vol 643 ◽  
pp. 83-89
Author(s):  
Shu Rong Sun ◽  
Guang Rong Zhang ◽  
Ping Zhao
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Switched Nonlinear Systems ◽  
Uniform Asymptotic Stability ◽  
Unstable Subsystems ◽  
The Stability

In this paper, we study the stability properties of a general class of nonautonomous discrete-time switched nonlinear systems. The switched systems consist of stable and unstable subsystems. Based on Lyapunov functions, some sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are established.

scholarly journals Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching

2010 ◽  
Vol 20 (3) ◽  
pp. 497-506 ◽  
Author(s):  
Zhengrong Xiang ◽  
Ronghao Wang ◽  
Qingwei Chen
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Switched Systems ◽  
Controller Design ◽  
Fault Tolerant ◽  
Fault Tolerant Control ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Switched Nonlinear Systems ◽  
Asynchronous Switching

Fault tolerant control of switched nonlinear systems with time delay under asynchronous switchingThis paper investigates the problem of fault tolerant control of a class of uncertain switched nonlinear systems with time delay under asynchronous switching. The systems under consideration suffer from delayed switchings of the controller. First, a fault tolerant controller is proposed to guarantee exponentially stability of the switched systems with time delay. The dwell time approach is utilized for stability analysis and controller design. Then the proposed approach is extended to take into account switched time delay systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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