Related papers: A Lyapunov function for fully nonlinear parabolic …
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify…
We construct an explicit Lyapunov function for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. We assume the nonlinearity is even in the advection term. We follow a method originally suggested by…
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…
Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.
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…
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 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…
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…
We apply a Lyapunov function to obtain conditions for the existence and uniqueness of small classical time-periodic solutions to first order quasilinear 1D hyperbolic systems with (nonlinear) nonlocal boundary conditions in a strip. 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…
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…
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…
The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…
Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…
Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous…
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…
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…
This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…