Positive system realizations

Abstract

Consider a rational discrete-time transfer function H(z) with the property that the associated causal impulse response h(k) is nonnegative for all k. A positive realization is a quadruple A, b, c, d such that

$$ H\left( z \right) = d + c{\left( {zI - A} \right)^{ - 1}}b $$

and all entries of A, b, c, d are nonnegative.

The author wishes to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program.