POLYNOMIAL METHODS FOR THE STRUCTURED SINGULAR VALUE WITH REAL PARAMETERS

摘要

We consider the structured singular value problem with real parametric uncertainty only. Using techniques from algebraic geometry, we propose two algorithms that in principle can yield the precise value of the structured singular value at a fixed frequency. Their ability to do so depends upon their ability to find all common roots to a system of polynomial equations. The first algorithm is applicable to problems with two real parameters each of multiplicity two. The second algorithm is applicable to problems with n distinct real parameters. These algorithms have proved useful in applications to aerospace control law analysis. [References: 26]