Robust performance of control systems containing parameter uncertainty

In this paper, control of linear systems with uncertain parameters is considered and a method is presented for the computation of allowable parameter perturbations to maintain stability and performance conditions. The desired performance is attained by putting frequency bounds on the sensitivity and the complementary sensitivity functions of the system in order to guarantee appropriate input tracking and sensor noise attenuation. The algorithm makes use of Neimark´s D-partition results on robust stability and extends the results to the case of robust performance. Explicit formulae are provided for performance measures, need to be minimized in a frequency range to compute the robust performance margin. The algorithm is then used in a controller synthesis procedure to design robust controllers in order to meet both stability and performance requirements. The details of the implementation of the procedure are illustrated through a case study.