The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.

By using concrete scenarios, we present and discuss a new concept of probabilistic Self-Stabilization in Distributed Systems.

Dijkstra’s concept of self-stabilization assumes that faults can only affect the variables of a program. We study the notion of self-stabilization if faults can also affect (i.e., augment) the program code of a system. A code stabilizing system automatically recovers from (almost) arbitrary perturbations of its program code. We prove some lower bounds for code stabilizing systems and argue that...

This paper deals with the practical robust stabilization and tracking problems of the perturbed multidimensional Heisenberg system with some additional integrators in the control input path. This objective is achieved by the use of variable structure control laws with an integral augmented sliding variable. This note shows how to select the integral sliding surface in such a way that the practi...

We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear optical waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even modes centered at finite distances from the surface and reveal the physical mechanism of the nonlinearity-induced stabilization of surface modes.

Let G be the group of projectivities stabilizing a unital U in PG(2, q2). In this paper, we prove that U is a classical unital if and only if there are two points in U such that the stabilizer of these two points in G has order q2 − 1.