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

Abstract

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.