Structural Properties of Maximally Robust Controllers

Abstract

This work contains results on properties of integrating feedback controllers which give maximal stability robustness against real coefficient uncertainty in the numerator and denominator coefficients of transfer functions of classes of linear discretetime scalar plants. The integrator imposes simply computed upper bounds on the size of the smallest destabilising plant numerator and denominator uncertainties. The ability for these bounds to be achieved for a given nominal plant depends on the existence of solutions of particular sign properties to interpolation problems. The first main result of this paper is to use these sign constraints to infer properties of the roots of corresponding controller polynomials. In particular it is shown how the robustness bound on denominator uncertainty cannot be achieved by a controller with any strictly unstable poles. The second main result concerns cancellation of nominal minimum phase plant zeros and its effect on robustness.