A fundamental multivariable robustness theorem for robust eigenvalue assignment

A fundamental robustness theorem for robust eigenvalue assignment of multivariable feedback systems is derived. The theorem determines whether a perturbed multivariable feedback system has its characteristic polynomial zeros located in the same regions as the nominal system does. It can be applied to continuous systems as well as to discrete systems. The theorem can handle nonsquare transfer matrices as well as dynamic output feedback. Conditions are discussed under which the proposed theorem reduces to a fundamental theorem for stability robustness analysis