Robust stability of complex systems with applications to performance attainment problems

Recently, a computationally efficient method was developed to deal with stability of a control system where the coefficients of the characteristic polynomial are polynomially dependent on the parameters of interest. In this paper, we extend this result to a family of complex polynomials which in turn solves some important performance attainment problems. This is due to the fact that a number of important performance attainment problems (phase margin, H_∞ margin, and SPR problem) can be cast as robust stability problems for complex polynomials. The results are illustrated by examples.