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Perturbation theory of observable linear systems

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Abstract

The present work is motivated by the asymptotic control theory for a system of linear oscillators: the problem is to design a common bounded scalar control for damping all oscillators in asymptotically minimal time. The motion of the system is described in terms of a canonical system similar to that of the Pontryagin maximum principle. We consider the evolution equation for adjoint variables as a perturbed observable linear system. Due to the perturbation, the unobservable part of the state trajectory cannot be recovered exactly. We estimate the recovering error via the L 1-norm of perturbation. This allows us to prove that the control makes the system approach the equilibrium state with a strictly positive speed.

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Correspondence to A. K. Fedorov.

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The article was submitted by the authors for the English version of the journal.

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Fedorov, A.K., Ovseevich, A.I. Perturbation theory of observable linear systems. Math Notes 98, 216–221 (2015). https://doi.org/10.1134/S0001434615070226

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  • DOI: https://doi.org/10.1134/S0001434615070226

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