Stability Analysis of Linear Coupled Differential-Difference Systems With General Distributed Delays

We present a new approach for the stability analysis of linear coupled differential-difference systems with a general distributed delay. The distributed delay term in this note can contain any L
²
function which is approximated via a class of elementary functions including polynomial, trigonometric, exponential functions, etc. Through the application of a new proposed integral inequality, a sufficient condition for the stability of the system is derived in terms of linear matrix inequalities based on the construction of a Lyapunov Krasovskii functional. The methods proposed in this note can handle problems that cannot be dealt using existing approaches. Two numerical examples are presented to show the effectiveness of our proposed stability condition.