State space analysis and optimal control of time delay systems via Taylor series

Two new Taylor series approaches are presented for the state space analysis of linear time-invariant delay systems. Both approaches yield an explicit expression for the state vector. This expression involves only the multiplication of matrices of small dimensions. No algebraic system of equations needs to be solved, and therefore no inversion of large matrices is required, as compared to other known techniques. Subsequently, these state space analysis results are used in solving the optimal control problem. The authors´ optimal control results give better accuracy.