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Mat. Zametki, Forthcoming paper (Mi mz10873)  

Perturbation theory of observable linear systems

A. K. Fedorov*, A. Ovseevich


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. Motion of the system is described in terms of a canonical system similar to that of the Pontryagin maximum principle. We consider 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 L1-norm of perturbation. This allows us to prove that the control makes the system approach the equilibrium with a strictly positive speed.

Keywords: linear system, controllability, observability
* Author to whom correspondence should be addressed

Received: 18.05.2015

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