Assignment of Characteristic Functions and a New Method for Stabilizing Multivariable Systems

A method for assigning characteristic functions on rational functions is presented herein. In systems with rational characteristic loci, input–output decoupling and commutative compensator design are possible. In this method, unlike previous research, which used the approximation method in a specific frequency range, a perturbation is created in the transfer function such that a new transfer function matrix has rational characteristic functions. It is shown that the stabilization of multivariate systems can be reduced to the stabilization of diagonal multivariate systems. Some examples of the implementation of the method are presented. The proposed method is not based on inverting the transfer function, so it is superior to inverse-based methods. The second priority of our approach is that the characteristic loci do not directly participate in the design process.