Structural instability of a class of decoupling solutions

This short paper is concerned with a class of decoupling solutions for linear dynamic systems of the type , with controller given by . The structural stability of solutions in this class is studied from a geometric viewpoint. The solution set defined here consists of points representing the controller gains and . It is found that most decoupling problems that are practically solvable-via known computational procedures-yield solution sets which are proper hypersurfaces in the control parameter spaces; hence, they form structurally unstable solutions in the sense that a solution will generally be forced out of this class when the system undergoes even quite small parameter variations.