A Sufficient Condition for the Almost Global Stability of Nonlinear Switched Systems with Average Dwell Time

2019 ◽  
Author(s):  
Ferruh Ilhan ◽  
Ozkan Karabacak ◽  
Rafael Wisniewski
Keyword(s):  
Global Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Sufficient Condition ◽  
Nonlinear Switched Systems

scholarly journals A Sufficient Condition for the Almost Global Stability of Nonlinear Switched Systems with Average Dwell Time

2019 ◽  
Author(s):  
Ferruh İlhan ◽  
Ozkan Karabacak ◽  
Rafael Wisniewski
Keyword(s):  
Global Stability ◽  
Upper Bound ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Sufficient Condition ◽  
Nonlinear Switched Systems

A sufficient condition for the almost global sta-bility of nonlinear switched systems under average dwell timerestriction is obtained. This condition is derived leaning uponthe existence of multiple Lyapunov densities, which are associ-ated to subsystems and satisfy some compatibility conditions.An upper bound for the average dwell time that ensures almostglobal stability is obtained.

Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs

2016 ◽  
Vol 40 (4) ◽  
pp. 1082-1091 ◽  
Author(s):  
Junqi Yang ◽  
Yantao Chen ◽  
Zheng Zheng ◽  
Wei Qian
Keyword(s):  
State Estimation ◽  
Switched Systems ◽  
Dwell Time ◽  
Sliding Mode ◽  
Lipschitz Constant ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Nonlinear Switched Systems ◽  
Continuous State

This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

scholarly journals Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Li ◽  
Xiaodi Li ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Switched Systems ◽  
Dwell Time ◽  
Lyapunov Method ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Nonlinear Switched Systems

This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.

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.

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