Design of p.d. controllers in linear multivariable systems

This paper deals with the design of proportional and derivative (p.d.) controllers in order to assign the poles of a linear multivariable system. It is shown that, for almost all reachable and observable systems given by a triplet (A,B,C), where A¿¿Rn.n, B¿¿Rn.r and C¿¿Rm.n, v poles can be assigned arbitrarily close to v specified symmetric values, where v= max {min(n, 2r + m¿¿ 1), min (n, 2m + r ¿¿ l)}¿¿l, with 1¿¿0, so that l degrees of freedom are disposable and can be used to locate the remaining n ¿¿ v poles in a specified region of the complex plane. Examples are included for illustration.