Robust control with structured perturbations

This paper considers the problem of robustification of a given stabilizing controller to make the closed loop system remain stable for prescribed ranges of variations of a set of physical parameters in the plant. The problem is treated in the state space and transfer function domains. In the state space domain a stability hypersphere is determined in the parameter space using Lyapunov theory. The radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere. In the transfer function domain a corresponding stability margin is defined and optimized based on the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial. The design algorithms are illustrated by examples.