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- W2951483067 abstract "We consider control systems of the type $dot x = A x +alpha(t)bu$, where $uinR$, $(A,b)$ is a controllable pair and $alpha$ is an unknown time-varying signal with values in $[0,1]$ satisfying a persistent excitation condition i.e., $int_t^{t+T}al(s)dsgeq mu$ for every $tgeq 0$, with $0<muleq T$ independent on $t$. We prove that such a system is stabilizable with a linear feedback depending only on the pair $(T,mu)$ if the eigenvalues of $A$ have non-positive real part. We also show that stabilizability does not hold for arbitrary matrices $A$. Moreover, the question of whether the system can be stabilized or not with an arbitrarily large rate of convergence gives rise to a bifurcation phenomenon in dependence of the parameter $mu/T$." @default.
- W2951483067 created "2019-06-27" @default.
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- W2951483067 date "2008-10-12" @default.
- W2951483067 modified "2023-09-27" @default.
- W2951483067 title "On the stabilization of persistently excited linear systems" @default.
- W2951483067 hasPublicationYear "2008" @default.
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