844 research outputs found
On feedback stabilization of linear switched systems via switching signal control
Motivated by recent applications in control theory, we study the feedback
stabilizability of switched systems, where one is allowed to chose the
switching signal as a function of in order to stabilize the system. We
propose new algorithms and analyze several mathematical features of the problem
which were unnoticed up to now, to our knowledge. We prove complexity results,
(in-)equivalence between various notions of stabilizability, existence of
Lyapunov functions, and provide a case study for a paradigmatic example
introduced by Stanford and Urbano.Comment: 19 pages, 3 figure
On convergence of infinite matrix products with alternating factors from two sets of matrices
We consider the problem of convergence to zero of matrix products
with factors from two sets of matrices,
and , due to a suitable choice of
matrices . It is assumed that for any sequence of matrices
there is a sequence of matrices such that the
corresponding matrix product converges to zero.
We show that in this case the convergence of the matrix products under
consideration is uniformly exponential, that is, , where the constants and
do not depend on the sequence and the corresponding sequence
.Comment: 7 pages, 13 bibliography references, expanded Introduction and
Section 4 "Remarks and Open Questions", accepted for publication in Discrete
Dynamics in Nature and Societ
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