scholarly journals Stability Analysis of Fractional Switched Systems With Stable and Unstable Subsystems

2021 ◽  
Author(s):  
Ran Yang ◽  
Song Liu ◽  
Xiaoyan Li ◽  
Jian Xiao
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Stability Conditions ◽  
Razumikhin Technique ◽  
Unstable Subsystems ◽  
Slow Switching

Abstract This article addresses stability of fractional switched systems (FSSs) with stable and unstable subsystems. First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. Then, some stability conditions which have less conservation are also provided by utilizing average dwell time (ADT) technique and the property of Mittag-Leffler function. In addition, sufficient conditions on asymptotic stability of delayed FSSs are obtained by virtue of fractional Razumikhin technique. Finally, several examples are given to reveal that the conclusions obtained are valid.

Stability analysis for discrete-time switched systems with uncertain time delay and affine parametric uncertainties

2016 ◽  
Vol 40 (4) ◽  
pp. 1150-1157 ◽  
Author(s):  
NA Baleghi ◽  
MH Shafiei
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Discrete Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Stability Conditions ◽  
Parametric Uncertainties ◽  
Switched Linear System ◽  
Uncertain Time

This paper studies the stability conditions of a discrete-time switched linear system in the presence of affine parametric uncertainties and an unknown time delay. Based on a discrete Lyapunov functional, sufficient conditions are investigated to determine the upper bound of admissible time delay in the discrete-time switched system. Furthermore, the average dwell time method, which is an effective tool for stability analysis of switched systems, is used to derive the exponential stability conditions. These conditions characterize the switching signal, which does not depend on any uncertainties. Finally, numerical examples are provided to verify and compare the theoretical results.

scholarly journals Stability Analysis of a Class of Switched Nonlinear Systems with an Improved Average Dwell Time Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rongwei Guo
Keyword(s):  
Stability Analysis ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Asymptotically Stable ◽  
Switched Nonlinear Systems ◽  
Globally Asymptotically Stable ◽  
Unstable Subsystems ◽  
Average Dwell Time Method ◽  
The Stability

This paper investigates the stability of switched nonlinear (SN) systems in two cases: (1) all subsystems are globally asymptotically stable (GAS), and (2) both GAS subsystems and unstable subsystems coexist, and it proposes a number of new results on the stability analysis. Firstly, an improved average dwell time (ADT) method is presented for the stability of such switched system by extending our previous dwell time method. In particular, an improved mode-dependent average dwell time (MDADT) method for the switched systems whose subsystems are quadratically stable (QS) is also obtained. Secondly, based on the improved ADT and MDADT methods, several new results to the stability analysis are obtained. It should be pointed out that the obtained results have two advantages over the existing ones; one is that the improved ADT method simplifies the conditions of the existing ADT method, the other is that the obtained lower bound of ADT (τa*) is also smaller than that obtained by other methods. Finally, illustrative examples are given to show the correctness and the effectiveness of the proposed methods.

scholarly journals Almost Global Stability of Nonlinear Switched System with Stable and Unstable Subsystems

2020 ◽  
Author(s):  
Aysegul Kivilcim ◽  
Ozkan Karabacak ◽  
Rafal Wisniewski
Keyword(s):  
Global Stability ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Operation Time ◽  
Average Dwell Time ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Unstable Subsystems ◽  
The Stability ◽  
Slow Switching

This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.

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