Delay-independent stability criteria under arbitrary switching of a class of switched nonlinear time-delay systems

Advances in Difference Equations

Marwen Kermani¹  Anis Sakly¹ 

[1] Research Unit of Industrial Systems Study and Renewable Energy (ESIER), National Engineering School of Monastir, Monastir, Tunisia

关键词: continuous switched nonlinear systems time delays;    global asymptotic stability;    Borne-Gentina criterion;    common Lyapunov function;    arrow form state matrix;    arbitrary switching;   

DOI  :  10.1186/s13662-015-0560-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper addresses the stability problem of a class of switched nonlinear time-delay systems modeled by delay differential equations. Indeed, by transforming the system representation under the arrow form, using a constructed Lyapunov function, the aggregation techniques, the Borne-Gentina practical stability criterion associated with the M-matrix properties, new delay-independent conditions to test the global asymptotic stability of the considered systems are established. In addition, these stability conditions are extended to be generalized for switched nonlinear systems with multiple delays. Note that the results obtained are explicit, they are simple to use, and they allow us to avoid the problem of searching a common Lyapunov function. Finally, an example is provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.

【 授权许可】

CC BY