Perturbation theory of observable linear systems

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.Comment: 7 pages; the subject of the present paper has grown out of study arXiv:1308.6090 (see Appendix V); published versio

Complete controllability of quantum systems

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio

Coherence resonance in a network of FitzHugh-Nagumo systems: interplay of noise, time-delay and topology

We systematically investigate the phenomena of coherence resonance in time-delay coupled networks of FitzHugh-Nagumo elements in the excitable regime. Using numerical simulations, we examine the interplay of noise, time-delayed coupling and network topology in the generation of coherence resonance. In the deterministic case, we show that the delay-induced dynamics is independent of the number of nearest neighbors and the system size. In the presence of noise, we demonstrate the possibility of controlling coherence resonance by varying the time-delay and the number of nearest neighbors. For a locally coupled ring, we show that the time-delay weakens coherence resonance. For nonlocal coupling with appropriate time-delays, both enhancement and weakening of coherence resonance are possible