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.

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.

Time-varying H∞ filtering for discrete-time switched systems with admissible edge-dependent average dwell time

2020 ◽  
Vol 42 (14) ◽  
pp. 2719-2732
Author(s):  
Bingxin Xue ◽  
Ruihua Wang ◽  
Shumin Fei
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Time Varying ◽  
Text Filtering ◽  
Exponentially Stable

This paper addresses the [Formula: see text] filtering problem for a class of discrete-time switched systems by using an admissible edge-dependent average dwell time (AED-ADT) method. By means of a convex combination of positive definite matrices, a novel multiple piecewise convex Lyapunov function (MPCLF) is constructed, which can loosen the restrictions of Lyapunov function at switching points and interval interior points. Based on the MPCLF approach, sufficient conditions are established such that the filtering error system is globally uniformly exponentially stable (GUES) and a prescribed noise attenuation level in an [Formula: see text] sense is achieved. Moreover, the corresponding time-varying [Formula: see text] filters are given as well. Finally, the results of the simulation illustrate the feasibility and effectiveness of the proposed approaches.

Stability and L2–Gain analysis of linear switched singular systems by using multiple discontinuous Lyapunov function approach

2019 ◽  
Vol 41 (15) ◽  
pp. 4197-4206 ◽  
Author(s):  
Jumei Wei ◽  
Huimin Zhi ◽  
Kai Liu
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Discrete Time ◽  
Text Analysis ◽  
Dwell Time ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Function Approach ◽  
Discrete Time Case

In this paper, the problem of the E-exponential stability and [Formula: see text] analysis of linear switched singular systems is investigated in discrete-time case. By using a multiple discontinuous Lyapunov function approach and adopting the mode-dependent average dwell time (MDADT) switching signals, new sufficient conditions of E-exponential stability and [Formula: see text] analysis for linear switched singular systems are presented. Based on the above results, we also derive the weighted [Formula: see text] performance index. In addition, by utilizing our proposed method, tighter bounds on average dwell time can be obtained for our considered systems. At last, a numerical example is given to show the effectiveness of the results.

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.

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