The positive (minimal) realization problem for a class of singular discrete-time linear single-input, single-output systems with delays in state and delays in control is addressed. Solvability conditions for the positive (minimal) realization problem are established. It is shown lat there exists a positive (minimal) realization of an improper transfer function T( z) = n( z) / d( z) if the coefficients of polynomial n( z) are on-negative and of the polynomial d( z) are non-positive except the leading one, which should be positive. A procedure for computation of le positive (minimal) realization of the transfer function is proposed and illustrated by an example.
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