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For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…

Dynamical Systems · Mathematics 2016-06-10 Leonid Berezansky , Elena Braverman , Lev Idels

We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Arnaud Munch , Lauri Oksanen

Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium…

Dynamical Systems · Mathematics 2022-08-22 Elena Braverman , Alexandra Rodkina

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…

Optimization and Control · Mathematics 2022-09-13 Michelle S. Chong

The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order $2 \times 2$ linear hyperbolic systems. The main technical point is to show that we…

Optimization and Control · Mathematics 2020-10-30 Long Hu , Guillaume Olive

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical…

Analysis of PDEs · Mathematics 2025-10-02 Xia Huang , Dong Ye

The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…

Systems and Control · Computer Science 2012-12-18 Zhuang Jiao , Yisheng Zhong

In the research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the…

Numerical Analysis · Mathematics 2019-12-19 Rémi Abgrall , Jan Nordström , Philipp Öffner , Svetlana Tokareva

This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…

Optimization and Control · Mathematics 2016-12-02 Helmut Gfrerer , Boris Mordukhovich

A new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a…

Numerical Analysis · Mathematics 2025-02-07 T. Lewis , X. Xue

Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…

Dynamical Systems · Mathematics 2018-08-29 Mark A. Pinsky , Steve Koblik

The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In oceanography it is known as the Alber equation, and its…

Numerical Analysis · Mathematics 2026-03-31 Agissilaos Athanassoulis , Fotini Karakatsani , Irene Kyza

In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…

Numerical Analysis · Mathematics 2020-10-20 He Li , Ian McInerney , James J. Davis , George A. Constantinides

In this work we determine the second-order coefficient in a parabolic equation from the knowledge of a single final data. Under assumptions on the concentration of eigenvalues of the associated elliptic operator, and the initial state, we…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki

The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…

Dynamical Systems · Mathematics 2010-01-27 Anca Veronica Ion

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and…

Dynamical Systems · Mathematics 2018-04-18 Alexis Arnaudon , Nader Ganaba , Darryl Holm

We use some properties of solutions of Riccati equation for establishing boundedness and stability criteria for solutions of second order linear ordinary differential equations. We show that the conditions on coefficients of the equations,…

Classical Analysis and ODEs · Mathematics 2019-05-17 G. A. Grigorian

There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…

Systems and Control · Electrical Eng. & Systems 2024-02-15 Jongrae Kim

Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a…

Optimization and Control · Mathematics 2022-05-09 Mathieu Bajodek , Frédéric Gouaisbaut , Alexandre Seuret

We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…

Optimization and Control · Mathematics 2012-09-21 Andrew P. Johnston , Serdar Yüksel