The stability of time-delay systems has been investigated in the last several decades. Stability criteria for linear time-delay systems can be divided into two categories, delay-independent stability criteria and delay-dependent stability criteria, by whether the criteria include the information about delays or not. In addition, linear time-delay systems can be divided into two categories by the number of delays. One are single-delay systems which have only a single time-delay constant and the other are multiple-delay systems which have at least two time-delay constants.
The delay-independent and delay-dependent stability criteria have been studied by many researchers. Delay-dependent stability criteria have improved the conservativeness of delay-independent stability criteria. Some Researchers proposed delay-dependent stability criteria by frequency domain approach and these criteria improved conservativeness of previous delay-independent criteria. In these days, many researchers suggested delay-dependent and delay-independent stability criteria as Linear Matrix Inequality(LMI) form to get less conservative stability criteria by Lyapunov functional approach.
We propose stability criteria for linear systems with time delays by employing the Lyapunov-Krasovskii functional approach and integral inequality. In the first part, stability criteria for the system with single delay is suggested. Then, we extend the results to the system with multiple delays. Finally, simulation results are given to be compared with the existing results in the literature.
A design method for the delay-dependent state feedback controller is proposed which guarantees the asymptotic stability of the linear uncertain systems with state and input delays based on Lyapunov-Krasovskii functional approach. The condition for the controller was given in terms of matrix inequalities including nonlinear terms. Because the original nonconvex feasibility problem is hard to solve, an it...