Delay-dependent stability condition for systems with distributed delays

The delay-dependent stability of a class of linear systems with distributed delays was investigated. By choosing proper Lyapunov function, delay-dependent stability conditions of this class of systems are formulated in terms of existence of positive definite solutions to a linear matrix equation. These conditions can be used to obtain a maximum allowable delay bound for the systems studied. These conditions are easy to be checked and can give a much less conservative delay bound than the existing methods. An example is given to show the efficiency of the obtained results.