ROBUST-CONTROL WITH STRUCTURED PERTURBATIONS
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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. These results differ from the previous treatment [1] of structured parameter perturbations where a linear relationship between the parameters and the closed-loop characteristic polynomial coefficients was assumed. No such assumption is made in this paper and in fact the closed-loop characteristic polynomial coefficients can be any function of the parameters. The design algorithms are illustrated by examples. 1988 IEEE
