Contents I. Introduction
Awell established technique for the design of linear multivariable systems is pole assignment. This is due to the fact that the stability and dynamic behavior of such systems are governed mainly by the pole locations of the closed-loop system. The first important results in pole assignment are reported in [1] proving that for an m-input, r-output system of order n, closed-loop poles can be assigned by static output feedback provided some mild conditions are satisfied. Methods to find the required feedback matrix are given in [2]–[3]. Many papers have dealt with sufficient or necessary conditions for the existence of the feedback matrix with varying degree of generality e.g. [4]–[6]. A state space procedure is given in [7] to assign min(n, mr) poles by static output feedback, which allows complete pole assignment for higher order multi-input multi-output systems since for these systems. More recently, attention has been focused on optimizing a performance index in addition to pole assignment for systems that have extra degrees of freedom in the form of excess parameters in the feedback matrix, see e.g. [8]–[10]. The optimization is usually taken as minimization of the sensitivity of closed-loop poles to perturbation or uncertainty in the system parameters.
