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One shows that the linearized Navier-Stokes equation in
, around an unstable equilibrium
solution is exponentially stabilizable in probability by an
internal noise controller , , where are
independent Brownian motions in a probability space and
is a system of functions on with
support in an arbitrary open subset . The
stochastic control input is found in feedback
form. One constructs also a tangential boundary noise controller
which exponentially stabilizes in probability the equilibrium
solution.
...
We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered.
Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.
The paper presents two methods used for the identification of Continuous-time Linear Time Invariant (CLTI) systems. In both methods the idea of using modulating functions and a convolution filter is exploited. It enables the proper transformation of a differential equation to an algebraic equation with the same parameters. Possible different normalizations of the model are strictly connected with different parameter constraints which have to be assumed for the nontrivial solution of the optimal...
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant.
The results are obtained by applying global perturbations of the domains
and exploiting analytic perturbation properties.
The work is motivated by two applications: an existence result for
the problem of maximizing the rate of...
Multivariable nonlinear systems with time delays are considered. The delays are supposed to be constant but not commensurate. The goal of this paper is to give a structure algorithm which displays some system invariants for this class of systems.
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