Related papers: Liapunov's direct method for Birkhoffian systems: …
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…
For systems evolving on a Riemannian manifold, we propose converse Lyapunov theorems for asymptotic and exponential stability. The novelty of the proposed approach is that is does not rely on local Euclidean coordinate, and is thus valid on…
We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…
The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by…
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…
This paper studies the uniformly asymptotic stability of nonautonomous systems on Riemannian manifolds. We establish corresponding Lyapunov-type theorems (Theorems 2.1 and 2.2), extending classical Euclidean results (e.g., [9, Theorems 4.9…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
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…
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…
For the $\mathfrak{so}(4)$ free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found we construct a…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this class, the significance of noncoercive Lyapunov functions is analyzed. It is shown that the existence of such Lyapunov functions implies…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…