Nonnegative realizations of matrix transfer functions Original Research Article

Various aspects of the nonnegative, finite-dimensional realizability of time-invariant discrete linear systems are considered. A new proof of the basic result of the nonnegative realizability of a primitive (scalar-valued) transfer function with nonnegative impulse response function is given. An algorithm for establishing whether a scalar-valued transfer function with nonnegative impulse response has a nonnegative realization is presented. The main result characterizes the nonnegative realizability of a scalar-valued transfer function with the help of primitive transfer functions, and is extended to the general case of matrix-valued transfer functions. Then conditions for the existence of some special nonnegative realizations of transfer functions are presented, e.g., where the middle (main) matrix is irreducible, strictly positive or primitive.