Optimal Control of Linear Time Invariant Singular Delay Systems Using the Orthogonal Functions

In this paper four different orthogonal functions have been used to approximate the optimal solution of linear time invariant (LTI) singular delayed systems. The idea is that the states and the input are expressed in terms of these orthogonal functions. The method simplifies the system of state equations into a set of algebraic equations which can be solved using a digital computer. The main advantage of the present work over other possible works is that, the present work shows using the Cosine series instead of Fourier series or by using Cosine wavelets instead of Sine-Cosine wavelets we get much more accurate results. The given examples support this claim.