Comparative analysis of simple improved delay-dependent stability criterions for linear time-delay systems: An augmented functional approach

In this paper a comparative analysis of simple improved delay-dependent stability criterions for linear time-delay systems is considered. In light of this comparison some new constructive sufficient conditions are derived. Based on augmented Lyapunov-Krasovskii functional combined with LMI's techniques except the existing a) simple α-stability criterion are proposed two new modification of b) simple improved stability and c) improved α-stability criterions. Other two new simple improved d) stability and e) α-stability criterions are considered by introducing special augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton formula and LMI's techniques. The results depend on the size of the delay and are given in terms of quadratic forms of state and LMI's, which are more informative and accurate, since the new combined techniques do not include any supplementary constraints on the system matrices. Thus, these types of criteria in general, are less conservative then the existing criteria and successfully avoided all existing problems. Comparative analysis of our stability result showed that the stability conditions are very well coordinated with one another. Memory less stabilization of linear time-delay systems also is considered.