Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems

2014 ◽  
Vol 15 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Xiao-li Zhang ◽  
An-hui Lin ◽  
Jian-ping Zeng
Keyword(s):  
Exponential Stability ◽  
Switched Systems ◽  
Unstable Subsystems ◽  
Impulsive Switched Systems

Globally exponential stability of nonlinear impulsive switched systems

2015 ◽  
Vol 97 (5-6) ◽  
pp. 803-810 ◽  
Author(s):  
F. Xu ◽  
L. Dong ◽  
D. Wang ◽  
X. Li ◽  
R. Rakkiyappan
Keyword(s):  
Exponential Stability ◽  
Switched Systems ◽  
Globally Exponential Stability ◽  
Impulsive Switched Systems

Stability of a class of nonlinear fractional order impulsive switched systems

2016 ◽  
Vol 39 (5) ◽  
pp. 781-790 ◽  
Author(s):  
Guopei Chen ◽  
Ying Yang
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Unstable Subsystems ◽  
Impulsive Switched Systems ◽  
The Stability ◽  
Work First ◽  
Periodic Switching

This paper considers the asymptotic stability of a class of nonlinear fractional order impulsive switched systems by extending the result of existing work. First, a criterion is given to verify the stability of systems by using the Mittag–Leffler function and fractional order multiple Lyapunov functions. Second, by combining the methods of minimum dwell time with fractional order multiple Lyapunov functions, another sufficient condition for the stability of systems is given. Third, by using a periodic switching technique, a switching signal is designed to ensure the asymptotic stability of a system with both stable and unstable subsystems. Finally, two numerical examples are provided to illustrate the theoretical results.

scholarly journals Robust exponential stability of nonlinear impulsive switched systems with time-varying delays

2012 ◽  
Vol 17 (2) ◽  
pp. 210-222 ◽  
Author(s):  
Xiu Liu ◽  
Shouming Zhong ◽  
Xiuyong Ding
Keyword(s):  
Exponential Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Lyapunov Functionals ◽  
Sufficient Condition ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Numerical Example ◽  
Impulsive Switched Systems ◽  
Theoretical Results

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results.

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.

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