Related papers: Stability Analysis of Fractional Differential Equa…
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…
We derive stability criteria for saddle points of a class of nonsmooth optimization problems in Hilbert spaces arising in PDE-constrained optimization, using metric regularity of infinite-dimensional set-valued mappings. A main ingredient…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…
The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
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…
We present some distinct asymptotic properties of solutions to Caputo fractional differential equations (FDEs). First, we show that the non-trivial solutions to a FDE can not converge to the fixed points faster than $t^{-\alpha}$, where…
This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…
Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by…
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
This paper investigates the stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics, modeled as interconnections of ordinary differential equations (ODEs) and hyperbolic partial…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…