Solving Interpolation Problems via Generalized Eigenvalue Minimization

A number of problems in the analysis and design of control systems may be reformulated as the problem Of minimizing the largest generalized eigenvalue of a pair of symmetric matrices which depend affinely on the decision variables, subject to constraints that are linear matrix inequalities. For these generalized eigenvalue problems, there exist numerical algorithms that are guaranteed to be globally convergent, have polynomial worst-case complexity, and stopping criteria that guarantee desired accuracy. In this paper, we show how a number of important interpolation problems in control may be solved via generalized eigenvalue minimization.