Robust Control in State Space: An Approach via the Krasovskii Theorem

The problem of robust control with structured perturbations is addressed in state space. Measures of preserving the closed-loop system stability for a given stabilizing controller with respect to parameter variations are determined in the parameter space using the Krasovskii stability theorem. Since the measures are directly given in terms of the nominal system matrix and perturbation structure matrix, solving the Lyapunov matrix equation required in approaches recently reported in the literature, is avoided. Based on the robust stability measure defined, an iterative design procedure is proposed to determine a robust controller for the perturbed system with prescribed range of perturbations. Numerical examples are also provided to illustrate the effectiveness of the results developed.