Delay-dependent stability and α-stability criterions for linear time-delay system

Some improved delay-dependent stability conditions for linear time-delay systems are considered by using augmented and special augmented Lyaounov-Krasovskii functionals combined with Leibniz-Newton formula, LMI's techniques and some integral evulating inequalities. The stability results are depend on the size of the delay term and are given in terms of quadratic forms of state and LMI's, which are more informative and accurate. Four simple examples are considered systematically to illustrate and comparision analysis of drived stability conditions. The upper bound of delay term are computed by solving quazi-convex optimization problem. Stabilization by memory less control is considered as five example, Comparision analysis show that drived stability conditions are less conservative than existing.