Technical Notes and Correspondence: A Fundamental Multivariable Robustness Theorem for Robust Eigenvalue Assignment

In this note, 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 the continuous systems as well as to the discrete systems. When the characteristic polynomial zeros are just requested to locate in the stable region, the proposed theorem would reduce to a fundamental theorem for stability robustness analysis.