characteristic functions assignment by adding perturbation

This paper presents a method for characteristic function assignment on rational functions by adding perturbation in systems with irrational characteristic functions. generally, in systems with irrational characteristic loci, commutative compensator designs are not possible. irrational characteristic functions have different forms. in our previous work, mentioned in the introduction section, a form of these characteristic functions was presented. another form of irrational characteristic functions is considered in this paper. this approach is not based on the transfer function inverting, and characteristic loci are not used directly in the design process. the efficacy of the proposed approach is investigated through two numerical examples.