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

A comparative analysis of simple improved delay-dependent stability criteria for linear time-delay systems is considered. In light of this comparison, some new constructive sufficient conditions are derived. Based on an augmented Lyapunov-Krasovskii functional combined with linear matrix inequality (LMI) techniques (apart from the existing simple α-stability criterion), I propose two new modifications of the simple improved stability and improved α-stability criteria. Two other two new simple improved stability and α-stability criteria are considered by introducing a special augmented Lyapunov-Krasovskii functional combined with the Leibniz-Newton formula and LMI techniques. The results depend on the size of the delay and are given in terms of quadratic forms of state and LMIs, 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 avoid all existing problems. A comparative analysis of our stability results shows that the stability conditions are very well coordinated with one another. Memoryless stabilization of linear time-delay systems is also considered