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Positive minimal realizations for singular discrete-time systems with delays in state and delays in control. (English) Zbl 1194.93128

Summary: 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 that 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 non-negative and of the polynomial \(d(z)\) are non-positive except the leading one, which should be positive. A procedure for computation of the positive (minimal) realization of the transfer function is proposed and illustrated by an example.

MSC:

93C55 Discrete-time control/observation systems
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