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Restricted real perturbation values with applications to the structured real controllability radius of LTI systems
Simon Lam and Edward J. Davison
Abstract
In this paper, the concept of "restricted real perturbation values" of a complex matrix triplet is introduced,
and a formula for computing lower bounds of these values is presented. Restricted real perturbation values are a
generalization of the real perturbation values introduced in (Bernhardsson, Rantzer, and Qiu, 1998),
which is a key concept in evaluating various
robustness radii found in the control literature, such as the real controllability/observability radius, the real
decentralized fixed-mode radius, the real minimum-phase radius, etc. The generalization to restricted real
perturbation values is needed for an extension of these radii to account for more general system perturbation
structures. As an example, we will use the results of this paper to compute the true value of the structured real
controllability radius of the multi-link inverted pendulum system. Also, we will numerically investigate cases of
when the provided lower bounds are achievable.
