Related papers: On the arbitrarily long-term stability of conserva…
This paper studies the contraction property of time-varying differential-algebraic equation (DAE) systems by embedding them to higher-dimension ordinary differential equation (ODE) systems. The first result pertains to the equivalence of…
We develop a deterministic large-time mechanism yielding Ces{\`a}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each observation interval, exact convexification on a compact…
This paper regards randomized discrete-time consensus systems that preserve the average "on average". As a main result, we provide an upper bound on the mean square deviation of the consensus value from the initial average. Then, we apply…
In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this system is exponentially stable under a condition on the…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…
In this paper we consider the stability and convergence of numerical discretizations of the Black-Scholes partial differential equation (PDE) when complemented with the popular linear boundary condition. This condition states that the…
The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…
This work considers a system coupling a viscous Burgers equation (aimed to describe a simplified model of $1D$ fluid flow) with the ODE describing the motion of a point mass moving inside the fluid. The point mass is possibly under the…
We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small perturbations can lead to large deviations over long times, while…
We consider the problem of network stability in finite-buffer systems. We observe that finite buffer may affect stability even in simplest network structure, and we propose an ordinary differential equation (ODE) model to capture the…
A key characteristic of the anomalous sub-solution equation is that the solution exhibits algebraic decay rate over long time intervals, which is often refered to the Mittag-Leffler type stability. For a class of power nonlinear…
The stabilization of nonlinear systems under zero-state-detectability assumption or its analogues is considered. The proposed supervisory control provides a finite time practical stabilization of output and it is based on uniting local and…
This paper proposes a new class of mass or energy conservative numerical schemes for the generalized Benjamin-Ono (BO) equation on the whole real line with arbitrarily high-order accuracy in time. The spatial discretization is achieved by…
The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…
We consider the problem of designing uniformly stable first-order optimization algorithms for empirical risk minimization. Uniform stability is often used to obtain generalization error bounds for optimization algorithms, and we are…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…
Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…