Recursive solution of systems modeled by state space and multi-delay systems via first and second order taylor series

The paper presents a recursive method using Taylor series to solve the states of time invariant control systems with and without delay. First of all, the Taylor series, both first and second order, are utilized to solve the state equation of a linear time invariant (LTI) system recursively. Subsequently, a recursive algorithm is proposed for solving an LTI system with delay. The states of the system solved using Taylor series are compared with exact solutions. The approach is much simpler than other established methods, and also, it proves to be reasonably accurate. The recursive algorithm presented avoids the use of any delay matrices. As expected, for same number of recursion steps, the second order Taylor series solution proves to be more efficient than the first order Taylor series approach. Examples are treated and the results obtained are presented via tables and graphs.