Integral equations depending analytically on a parameter

Stochastic Volterra integral equations with a parameter

Averaged control and observation of parameter-depending wave equations

We analyze the problem of averaged observability and control of wave equations. This topic is motivated by the control of parameter-dependent systems of wave equations. We look for controls ensuring the controllability of the averages of the states with respect to the parameter. This turns out to be equivalent to the problem of averaged observation in which one aims at recovering the energy of ...

Positive Periodic Solutions of Nonautonomous Functional Differential Equations Depending on a Parameter

where a = a(t), h = h(t), and τ = τ(t) are continuous T-periodic functions. We will also assume that T > 0, λ > 0, f = f (t) as well as h = h(t) are positive, ∫T 0 a(t)dt > 0. Functional differential equations with periodic delays appear in a number of ecological models. In particular, our equation can be interpreted as the standard Malthus population model y′ = −a(t)y subject to perturbation w...

On the factorization of rational matrices depending on a parameter

In 1961 Youla published his paper 'On the factorization of rational matrices'. He proved that any proper rational parahermitian matrix, positive definite on the imaginary axis can be factorized as the product of a proper rational matrix, stable with respect to the closed right half plane, and its adjoint. In this paper I prove that for any positive definite, nonstrictly proper matrix this facto...

Balanced model order reduction for systems depending on a parameter

We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel expressions for the form of second order corrections for singular values and singular vectors. The final result of our procedure is an order reduced model which...