Abstract
The orders of infinite zeros, defined as the orders of zeros of G(1/λ) at λ=0, where G(s) is the given system transfer function matrix, are important parameters in the linear system analysis.
In this paper, we investigate the generic orders of infinite zeros for multivariable structured systems. By a structured system we mean a linear, time invariant system, whose coefficient matrices contain some fixed zero elements. It is assumed that the elements other than fixed zeros may vary independenty of one another and take any real value except zero. The generic orders are orders for almost every possible set of values of the variable elements.
The signal flow graph and a modification of the Mason's formula have been used. It is observed that the generic orders of infinite zeros are obtained from the minimum number of integrators included in a separate set of forward paths between k pairs of inputs and outputs, k=1, 2, …, σ, where σ is the rank of the system transfer function. Furthermore it is possible to select such pairs with nesting property, that is, the (k-1) pairs used to obtain first smallest (k-1) orders are included in k pairs for obtaining the k-th smallest order. Finally a sufficient condition is derived for the order of infinite zeros to be identical for every possible set of values of variable elements.
