Related papers: Transient dynamics under structured perturbations:…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
Matrix perturbation bounds (such as Weyl and Davis-Kahan) are used abundantly in many areas of mathematics and data science. Many bounds (such as the above two) involve the spectral norm of the noise matrix and are sharp in worst case…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
This paper discusses differential stability of convex programming problems in Hausdorff locally convex topological vector spaces. Among other things, we obtain formulas for computing or estimating the subdifferential and the singular…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
We consider a rank-one symmetric matrix corrupted by additive noise. The rank-one matrix is formed by an $n$-component unknown vector on the sphere of radius $\sqrt{n}$, and we consider the problem of estimating this vector from the…
This paper studies stability and symmetry preserving $H^2$ optimal model reduction problems of linear systems which include linear gradient systems as a special case. The problem is formulated as a nonlinear optimization problem on the…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
Asymptotic dynamics of ordinary differential equations (ODEs) are commonly understood by looking at eigenvalues of a matrix, and transient dynamics can be bounded above and below by considering the corresponding pseudospectra. While…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
As an indicator of the stability of spectral clustering of an undirected weighted graph into $k$ clusters, the $k$th spectral gap of the graph Laplacian is often considered. The $k$th spectral gap is characterized in this paper as an…
This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices. From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate…
This paper focuses on the construction of differential-cascaded structures for control of nonlinear robot manipulators subjected to disturbances and unavailability of partial information of the desired trajectory. The proposed…