Nonnegative realizations of matrix transfer functions

Various aspects of the nonnegative, finite-dimensional realizability of tim e-invariant discrete linear systems are considered. A new proof of the basi c result of the nonnegative realizability of a primitive (scalar-valued) tr ansfer function with nonnegative impulse response function is given. An alg orithm for establishing whether a scalar-valued transfer function with nonn egative impulse response has a nonnegative realization is presented. The ma in result characterizes the nonnegative realizability of a scalar-valued tr ansfer function with the help of primitive transfer functions, and is exten ded to the general case of matrix-valued transfer functions. Then condition s for the existence of some special nonnegative realizations of transfer fu nctions are presented, e.g., where the middle (main) matrix is irreducible, strictly positive or primitive. (C) 2000 Elsevier Science Inc. All rights reserved.