Algorithm to produce a system of type number m using state variable feedback

Describes a searching algorithm, based on the Routh array, to determine the unknown coefficients of a Hurwitz polynomial A¯(s) of degree n, where polynomial P(s) of degree m-1(m-1<n) is given and determines the first m coefficients. Sufficient conditions are derived to ensure that no solution exists, and a criterion of failure of the search is also derived and is shown to be both necessary and sufficient. Some examples are given, and it is demonstrated that increasing the number of restrictions on the ranges of the search increases the speed of solution and the number of solutions found. It is also shown that increasing the number of trials (N_p) increases the time taken and the number of solutions found. The examples illustrate how the given polynomial P(s) restricts the range of values of the unknown coefficients and how, in particular, this may lead to a need for very large or very small gains for implementation of state variable feedback