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Research Papers

Robust Stability of Switched Interconnected Systems With Time-Varying Delays

[+] Author and Article Information
Huanbin Xue

School of Mechanics and Engineering,
Southwest Jiaotong University,
No. 111, the Second Ring Road,
Chengdu 610031, Sichuan, China;
College of Mathematics and Statistics,
Hanshan Normal University,
Qiaodong,
Chaozhou 521041, Guangdong, China
e-mail: huanbinxue@163.com

Jiye Zhang, Baoshan Jiang

State Key Laboratory of Traction Power,
Southwest Jiaotong University,
No. 111, the Second Ring Road,
Chengdu 610031, Sichuan, China

Hong Wang

School of Mechanics and Engineering,
Southwest Jiaotong University,
No. 111, the Second Ring Road,
Chengdu 610031, Sichuan, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 10, 2017; final manuscript received September 30, 2017; published online November 1, 2017. Assoc. Editor: Zaihua Wang.

J. Comput. Nonlinear Dynam 13(2), 021004 (Nov 01, 2017) (10 pages) Paper No: CND-17-1204; doi: 10.1115/1.4038203 History: Received May 10, 2017; Revised September 30, 2017

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and time-varying delays is investigated. On the assumption that each isolated subsystem of the interconnected system can be exponentially stabilized and the corresponding Lyapunov functions are available, using M-matrix property, the differential inequalities with time-varying delays are constructed. By the stability analysis of the differential inequalities, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems (SIS) under arbitrary switching are obtained. The proposed method, which neither requires the individual subsystems to share a common Lyapunov function (CLF), nor needs to know the values of individual Lyapunov functions at each switching time, would provide a new mentality for studying stability of arbitrary switching. In addition, by resorting to average dwell time approach, conditions for guaranteeing the robust exponential stability of SIS under constrained switching are derived. The proposed criteria are explicit, and they are convenient for practical applications. Finally, two numerical examples are given to illustrate the validity and correctness of the proposed theories.

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Figures

Grahic Jump Location
Fig. 1

Δ=∩k=12Ω(Qk) of the considered switched system for Example 1

Grahic Jump Location
Fig. 2

State responses of the subsystem 1 of the considered switched system for Example 1

Grahic Jump Location
Fig. 3

State responses of the subsystem 2 of the considered switched system for Example 1

Grahic Jump Location
Fig. 4

State responses of the considered switched system for Example 1 with average dwell time Γ1<Γ*

Grahic Jump Location
Fig. 5

State responses of the considered switched system for Example 1 with average dwell time Γ2>Γ*

Grahic Jump Location
Fig. 6

Δ=∩k=12Ω(Qk) of the considered switched system for Example 2

Grahic Jump Location
Fig. 7

State responses of the considered switched system for Example 2

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