相关论文: Stability in controlled L-theory

We characterise subcategories of semistable modules for noncommutative minimal models of compound Du Val singularities, including the non-isolated case. We find that the stability is controlled by an infinite polyhedral fan that stems from…

The paper is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c, 0) of the Euler system there is a control which is…

We consider the problem of boundary control for a vibrating string with $N$ interior point masses. We assume the control is at the left end, and the string is fixed at the right end. Singularities in waves are "smoothed" out to one order as…

Controlled algebra plays a central role in many recent advances in geometric topology. This paper studies the iteration construction that was present from the very origins of the theory but started being exploited only recently. We develop…

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |X X \^{-1} X |/ |X| bounded is…

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.

The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary…

This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Math\'ematiques et applications at Sorbonne University, delivered over the past few years.…

In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…

We study the character theory of metabelian and polycyclic groups. It is used to investigate Hilbert-Schmidt stability via the character-theoretic criterion of Hadwin and Shulman. There is a close connection between stability and dynamics…

The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…

This is the first part of a series of papers devoted to the study of linear cocycles over chaotic systems. In the present paper, we establish the existence of such cocycles that $\mathcal{C}^\alpha$-stably exhibit fiberwise bounded orbits…

We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to…

We prove Hida-style control theorems in the derived setting for a large class of reductive groups tailored for applications to Euler systems.

Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…

In this article we prove semiglobal stabilization and exact controllability results for nonlinear plate equations with hinged boundary conditions and analytic nonlinearity. These results hold when the damping or control is localized in a…

This work develops a symmetry-based framework for formation control on cycle graphs using Dihedral point-group constraints. We show that enforcing inter-agent reflection symmetries, together with anchoring a single designated agent to its…

This paper is concerned with exponential stability of a class of infinite dimensional coupled systems. It is proved that under some admissibility conditions, the considered infinite dimensional coupled system is governed by a…

We study the boundary control problems for the wave, heat, and Schr\"odinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting…

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…