Abdelaziz Rhandi

Positive Linear Systems

We present one important large field of applications to the theory developed so far: control theory. More specifically, we present an elementary introduction to positive linear systems.

Feedback theory for time-varying regular linear systems with input and state delays

We show that the class of regular time-varying systems is invariant under perturbations by time-varying state and input delays. In particular, we give explicit formulas of the resulting input, output and input-output maps. This result is used to solve the feedback problem for the delayed system. The relationship between the open- and the closed-loop system is investigated. Our results are applied to a parabolic boundary control problem with input and state delays.

A Characterization of Lipschitz Continuous Evolution Families on Banach Spaces

We consider evolution families (U(t, s)) of bounded, linear operators on a Banach space X and associate to it an evolution semigroup (T(t)) t≥0 defined by

Kernel Estimates for Nonautonomous Kolmogorov Equations with Potential Term

T(t)f(s) = U(s,s - t)f(s - t)

Elliptic operators with unbounded diffusion coefficients perturbed by inverse square potentials in

on the weighted function space C υ0(ℝ, X). In the case of Lipschitz continuity of (U(t, s)) we characterize the generator of this semigroup (T(t)) t≥0 and thus obtain a family of operators A(t) ∈ ℒ(X) such that (U(t,s)) solves the non-autonomous Cauchy problem

--spaces

\dot{u} = A(t)u(t),u(s) = {{u}_{0}}.