LMI formulations for designing controllers according to time response and stability margin constraints

Designing a controller with respect to time and frequency-domain objectives remains a difficult problem, although both kinds are generally present in the manufacturer specifications. In general, the temporal objectives are replaced by frequency dependent ones, which in major cases do not fit the actual expectations. In this paper, convex mathematical translations of both kinds of objectives are proposed using Linear Matrix Inequalities (LMI). The application of Youla parameterization allows to restore the linearity in the compensator parameters, but a huge state space representation of the system is induced. Thus the Cutting Plane Algorithm (CPA) is efficiently used to overcome the problem of having a huge number of added variables, which often occurs in Semi-Definite Programming (SDP) particulary when used in conjunction with the Youla parameterization.