Stability and numerical solution of time variant linear systems with delay in both the state and control

In this paper, stability for uncertain time variant linear systems with time delay is studied. A new sufficient condition for delay-dependent systems is given in matrix inequality form which depends on the range of delay. Then, we introduce a new direct computational method to solve delay systems. This method consists of reducing the delay problem to a set of algebraic equations by first expanding the candidate function as hybrid functions with unknown coefficients. By using collocation method, the coefficients of the hybrid functions are obtained. Some numerical examples are given to illustrate and compare our results with other existing methods in the literature.