Sum of roots, polynomial spectral factorization, and control performance limitations

It has been pointed out that the notion of the sum of roots can be utilized for solving (parametric) polynomial spectral factorization. This paper reveals another aspect of the sum of roots as an indicator of achievable performance limitations. It is shown that performance limitations for some H₂ control problems can be expressed as the difference of two sums of roots. An optimization approach combining the two aspects of the sum of roots is also demonstrated that minimizes the achievable performance limitation over plant parameters.