LMI stability criterion with less variables for time-delay systems

Slack variables approach is an important technique for tackling the delay-dependent stability problem for systems with time-varying delay. In this paper, a new delay-dependent stability criterion is presented without introducing any slack variable. The technique is based on a simply integral inequality. The result is shown to be equivalent to some existing ones but includes the least number of variables. Thus, redundant selection and computation can be avoided so that the computational burden can be largely reduced. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions.