Improvement of parametric stability margin under pole assignment

In this paper, the improvement of the parametric stability margin of state-space uncertain systems via a maximization formulation under the constraints of pole assignment is investigated. The class of systems considered is where the uncertainty may be modeled as the, possibly nonlinear, variation of a parameter appearing in the entries of the system and input matrices. The continuity and differentiability properties of the stability margin are discussed. A gradient-based approach is presented for the improvement of the stability margin and a compact formula to compute the gradient is provided. Numerical examples are used to demonstrate the effectiveness of the approach.