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Home  >  Volume 26 (March 2014)

8. Optimal Expressions for Control Index Matrices fora Class of Double – Delay Differential Systems by C. Ukwu And E.J.D. Garba. Volume26, (March, 2014), pp 36 – 45.
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Abstract

This paper derived the structure of the indices of control systems for a class of double – delay autonomous linear differential systems on any given interval of length equal to the delay h for non –negative time periods. The formulation and the development of the theorem exploited an earlier work by Ukwu [1] on the interval   

The development of the associated solution matrices exploited the continuity of these matrices for positive time periods, the method of steps and backward continuation recursions to obtain these matrices on successive intervals of length equal to the delay h.  The proof was achieved using ingenious combinations of summation notations, greatest integer functions, and multiple integrals to obtain these matrices on successive intervals of length equal to the delay h. 

The indices were derived using the stage – wise algorithmic format, starting from the right – most interval of length h. This theorem globally extends the time scope of applications of these matrices to the solutions of terminal function problems and rank conditions for controllability.

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