A Q-matrix implementation of the Boxer and Thaler Z-form method

Application of the impulse invariance technique to
z
-transformation of certain Laplace transfer functions can be difficult if the function is not reduced to a constituent partial fraction form. This may be overcome by use of the
z
-form method, originally proposed by Boxer and Thaler [1]. However, the technique often requires a substantial amount of algebraic manipulation.
Q
-matrix methods are widely employed for such applications involving the bilinear transformation and substantially reduce the required amount of manipulation. This paper presents a general method for the formation and application of a
z
-form
Q
-matrix.