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.

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.

Observability and Distinguishability Properties and Stability of Arbitrarily Fast Switched Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Najah F. Jasim
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
External Disturbances ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Arbitrary Switching

This paper addresses sufficient conditions for asymptotic stability of classes of nonlinear switched systems with external disturbances and arbitrarily fast switching signals. It is shown that asymptotic stability of such systems can be guaranteed if each subsystem satisfies certain variants of observability or 0-distinguishability properties. In view of this result, further extensions of LaSalle stability theorem to nonlinear switched systems with arbitrary switching can be obtained based on these properties. Moreover, the main theorems of this paper provide useful tools for achieving asymptotic stability of dynamic systems undergoing Zeno switching.

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 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.

scholarly journals Exponential Stabilization for a Class of Nonlinear Switched Systems with Mixed Delays under Asynchronous Switching

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yongzhao Wang
Keyword(s):  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Schur Complement ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Asynchronous Switching ◽  
Nonlinear Switched Systems ◽  
Switched Nonlinear System

This paper deals with the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching. The switching signal of the switched controller involves delay, which results in the asynchronous switching between the candidate controllers and subsystems. By constructing the parameter-dependent Lyapunov-Krasovskii functional and the average dwell time approach, some sufficient conditions in forms of linear matrix inequalities are presented to ensure the exponential stability of the switched nonlinear system under arbitrary switching signals. In addition, through the special deformation of the matrix and Schur complement, the controllers with asynchronous switching are designed. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results.

The stability analysis of nonlinear switched systems with time delay in input and states with stable and unstable subsystems

2018 ◽  
Vol 40 (16) ◽  
pp. 4298-4308 ◽  
Author(s):  
Zeinab Echreshavi ◽  
Alireza Roosta
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Switched System ◽  
Control Laws ◽  
Nonlinear Switched Systems ◽  
Unstable Subsystems ◽  
Measurement Delay ◽  
The Stability ◽  
System With Time Delay

Time delay and sampling appear in many industrial systems. It is irrefutable that applying measurement delay with controls can cause the sampling of control laws with the delay in the behavior of nonlinear control systems. As a result, in this paper, the stability of nonlinear time varying switched system with time delay in the input and the states of the system is studied in two modes by a new Lyapunov Krasovskii functional (LKF). Firstly, if all subsystems of the proposed nonlinear switched system with time delay are stable. Then, if some of the subsystems of the proposed switched system are unstable. This paper is organized in two steps. In the first step, the upper bound for the time delay under sufficient conditions in the nonlinear systems with time delay in input and states is obtained. In this step, the Uniformly Globally Asymptotic Stability is proved for nonlinear systems with the presence of time delay. In the second step, with a proper Lyapunov Krasovskii functional, the global exponential stability of the proposed switched system is proved. Also, finally a proper observer is designed for our proposed switched system in two stable and unstable modes.

scholarly journals Stabilization of a Class of Continuous-Time Switched Systems with State Constraints via a Mode-Dependent Switching Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Qingyu Su ◽  
Peipei Wang
Keyword(s):  
Continuous Time ◽  
Switched Systems ◽  
Dwell Time ◽  
State Constraints ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Decay Rates ◽  
Average Dwell Time Method ◽  
The Stability ◽  
Switching Method

The stability and the stabilization problems for a class of continuous-time switched systems with state constraints via a mode-dependent switching method are investigated. The paper presents an improved average dwell time method, which considers different decay rates of a Lyapunov function related to each of the active subsystems according to whether the saturations occur or not, respectively. It is shown that the improved average dwell time method is less conservative than the common average dwell time method. Based on the improved average dwell time method, the sufficient conditions and state feedback controllers for stabilization of the switched system are derived. A numerical example is given to illustrate the proposed approach.

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