Related papers: Approximating the nearest stable discrete-time sys…
We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
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…
We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for which a "good" macroscopic description in the form of…
We revisit the numerical stability of four well-established explicit stochastic integration schemes through a new generic benchmark stochastic differential equation designed to assess asymptotic statistical accuracy and stability…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
The problem of stabilization of unstable periodic orbits of discrete nonlinear systems is considered in the article. A new generalization of the delayed feedback, which solves the stabilization problem, is proposed. The feedback is…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…
This paper studies the well-posedness and regularity of safe stabilizing optimization-based controllers for control-affine systems in the presence of model uncertainty. When the system dynamics contain unknown parameters, a finite set of…
We study the problem of finding the nearest $\Omega$-stable matrix to a certain matrix $A$, i.e., the nearest matrix with all its eigenvalues in a prescribed closed set $\Omega$. Distances are measured in the Frobenius norm. An important…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…
The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear…
We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not…