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The internal stabilization by noise of the linearized Navier-Stokes equation*

Viorel Barbu (2011)

ESAIM: Control, Optimisation and Calculus of Variations

One shows that the linearized Navier-Stokes equation in 𝒪 R d , d 2 , around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller V ( t , ξ ) = i = 1 N V i ( t ) ψ i ( ξ ) β ˙ i ( t ) , ξ 𝒪 , where { β i } i = 1 N are independent Brownian motions in a probability space and { ψ i } i = 1 N is a system of functions on 𝒪 with support in an arbitrary open subset 𝒪 0 𝒪 . The stochastic control input { V i } i = 1 N is found in feedback form. One constructs also a tangential boundary noise controller which exponentially stabilizes in probability the equilibrium solution. ...

The relationship between the infinite eigenvalue assignment for singular systems and the solvability of polynomial matrix equations

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

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 role of parameter constraints in EE and OE methods for optimal identification of continuous LTI models

Witold Byrski, Jedrzej Byrski (2012)

International Journal of Applied Mathematics and Computer Science

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 squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

Yannick Privat, Mario Sigalotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

The structure of nonlinear time delay systems

Luis Alejandro Márquez-Martínez, Claude H. Moog, Martín Velasco-Villa (2000)

Kybernetika

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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