相关论文: Robust Lyapunov Functions for Reaction Networks: A…

In this paper, we study the consensus problem for networked dynamic systems with arbitrary initial states, and present some structural characterization and direct construction of consensus functions. For the consensus problem under similar…

We provide a constructive proof on the equivalence of two fundamental concepts: the global Lyapunov function in engineering and the potential function in physics, establishing a bridge between these distinct fields. This result suggests new…

This article investigates the consensus tracking problem of multi-agent systems under jointly connected topology through automated synthesis of Lyapunov functions. Based on the proposed distributed nonlinear control protocol, several…

Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for constructing explicit ranges where quadratic Lyapunov functions…

Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…

This paper proposes several Converse Lyapunov Theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of corresponding Lyapunov functions in a normal neighborhood of an…

Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…

We introduce the notion of non-oscillation, propose a constructive method for its robust verification, and study its application to biological interaction networks (also known as, chemical reaction networks). We begin by revisiting…

As more inverter-connected renewable resources are integrated into the grid, frequency stability may degrade because of the reduction in mechanical inertia and damping. A common approach to mitigate this degradation in performance is to use…

We address the problem of Lyapunov function construction for a class of continuous-time Markov chains with affine transition rates, typically encountered in stochastic chemical kinetics. Following an optimization approach, we take advantage…

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…

While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…

Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation.…

Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for…

The dynamics of fluctuations is considered for electrons near a positive ion or for charges in a confining trap. The stationary nonuniform equilibrium densities are discussed and contrasted. The linear response function for small…

This paper studies the relationship between the Lyapunov function of a macrosystem whose dynamics is governed by the laws of stochastic chemical kinetics and the invariant measure of this macrosystem arising at large times. A necessary and…

This article presents a novel numerically tractable technique for synthesizing Lyapunov functions for equilibria of nonlinear vector fields. In broad strokes, corresponding to an isolated equilibrium point of a given vector field, a…

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…

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…