相关论文: Lyapunov Function Partial Differential Equations f…
Lyapunov functions are fundamental to establishing the stability of Markovian models, yet their construction typically demands substantial creativity and analytical effort. In this paper, we show that deep learning can automate this process…
In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial dimension coupled with a set of Ordinary Differential…
We present three examples of chemical reaction networks whose ordinary differential equation scaling limit are almost identical and in all cases stable. Nevertheless, the Markov jump processes associated to these reaction networks display…
A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…
Khasminski's \cite{chas1980stochastic} showed that many of the asymptotic stability and the integrability properties of the solutions to the Stochastic Differential Equations (SDEs) can be obtained using Lyapunov functions techniques. These…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the…
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…
This paper studies the input-to-state stability (ISS) properties based on the method of Lyapunov functionals for a class of semi-linear parabolic partial differential equations (PDEs) with respect to boundary disturbances. In order to avoid…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…
We consider delayed chemical reaction networks with generalized kinetics of product form and show that complex balancing implies that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is…
This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
This tutorial provides an overview of the generalized Lyapunov method (GLM) for analyzing input-to-state stability (ISS) of partial differential equations (PDEs). We begin by revisiting the classical Lyapunov method and the standard…
In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…