Abstract
The robust stabilization of linear systems with constant uncertainties against structured perturbations using Lyapunov's theory is investigated. The only information needed on the uncertainties is the knowledge of their boundaries. The matching conditions of the uncertain systems are not required to be satisfied. It is first shown that, under some assumptions, the system can be transformed into a certain canonical controllable companion form. Then, under some additional assumptions, the existence of a linear controller which stabilizes the system based on Lyapunov's theory is shown.
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Chao, C.H., Stalford, H.L. On the robustness of linear stabilizing feedback control for linear uncertain systems: Multi-input case. J Optim Theory Appl 64, 229–244 (1990). https://doi.org/10.1007/BF00939447
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DOI: https://doi.org/10.1007/BF00939447