Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay

Lien, Chang‐Hua; Yu, Ker‐Wei; Chung, Yeong-Jay; Chang, Hao‐Chin; Chen, Jenq-Der

doi:10.1016/j.nahs.2010.08.002

Cited by 47 publications

(51 citation statements)

References 9 publications

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“…Consequently, wide efforts have been devoted to address the challenge of switched systems with time varying delays [10,11,13,16,17,19,[22][23][24][25][26]. In addition, from the practical standpoint, it is important to tackle uncertain 2 Mathematical Problems in Engineering switched systems [18,19,23,25,26].…”

Section: Introductionmentioning

confidence: 99%

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On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

Kermani

Sakly

2018

Mathematical Problems in Engineering

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This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

“…Up to now, there are few results concerning stability analysis of uncertain switched nonlinear systems with time varying delays under arbitrary switching [23]. Thus, almost all existing works deal with the linear case or the linearization of the original nonlinear systems by using the TS fuzzy models [19,20].…”

Section: Introductionmentioning

confidence: 99%

On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

Kermani

Sakly

2018

Mathematical Problems in Engineering

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“…This switching rule is usually a function that depends on the time or the state. We call it a switching function, a switching law, or a switching signal (Lien, 2011). At present, the research of switched systems has become a hot issue in modern control theory, and has made some achievements (Sun, 2006;Zhang,2013).…”

Section: Introductionmentioning

confidence: 99%

Study on the Stability of Switched Systems based on Uncertain Nonlinear Time Delay

2017

Revista Tecnica De La Facultad De Ingenieria Universidad Del Zu

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Switching system is very important in the fields of industrial manufacture, chemical process, intelligent control, which have attracted much attention in recent years. It is well known that the phenomenon of time delay and nonlinear disturbance exist in the actual switching system, so the research on nonlinear time delay switched systems has great theoretical significance and practical value. In this paper, we discuss the exponential stability of a class of switched systems with nonlinear perturbations, and then derive the stability conditions by using the theory of integral inequality and the average dwell time. From the actual research model of switching system, most of the system is unstable, so it is very important to design a switching strategy which can make the system stable

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“…Some examples for switched systems are automated highway systems, automotive engine control system, chemical process, constrained robotics, power systems and power electronics, robot manufacture, and stepper motors . It is also well known that the existence of delay in a system may cause instability or bad www performance in closed control systems [2][3][4][5][6][7][8][9][10][11][12][13][14]17,18,23,24,[26][27][28]. Time-delay phenomena are usually encountered in many practical systems, such as AIDS epidemic, aircraft stabilization, chemical engineering systems, hydraulic systems, inferred grinding model, manual control, neural network, nuclear reactor, population dynamic model, rolling mill, ship stabilization, and systems with lossless transmission lines.…”

Section: Introductionmentioning

confidence: 99%

“…Another interesting fact is that the stability of a switched system can be achieved by choosing the switching signal even when each subsystem is unstable [2,8,10,11,14]. In [10], a switching signal design technique is proposed to guarantee the asymptotic stability of discrete switched systems with interval time-varying delay.…”

Section: Introductionmentioning

confidence: 99%

Switching signal design for exponential stability of discrete switched systems with interval time-varying delay

Lien

Chang

et al. 2012

Journal of the Franklin Institute

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Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay

Cited by 47 publications

References 9 publications

On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

Study on the Stability of Switched Systems based on Uncertain Nonlinear Time Delay

Switching signal design for exponential stability of discrete switched systems with interval time-varying delay

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