Stability problems in using state variable feedback to produce a servomechanism of specified type number

The problem of constructing a Hurwitz polynomial Â( s) of degree n, under the condition that the coefficients up to and including that of 8^m?1 are given, is discussed, Root locus arguments are used to establish necessary and sufficient conditions for stabilizability with m = l, 2, 3 and sufficient conditions for m > 3. A Routh array approach yields necessary and sufficient conditions for m = 4 and a general method of attack for m > 4 The origin of the problem (in the design of tracking servo-mechanisms) is explained, and a procedure for producing a system with specified type number is outlined.