An algorithm for pole assignment in high order multivariable systems

An efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions. A given multiinput system is first transformed to an upper block Hessenberg form by means of orthogonal state coordinate transformations. The state feedback problem is then reformulated in terms of the Sylvester equation. The transformed system matrices, along with certain assumed block forms for unknown matrices, enable the Sylvester equation to be decomposed and solved effectively. A distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast. Computational aspects of the algorithm are discussed and numerical examples are provided