Related papers: Almost Lyapunov Functions for Nonlinear Systems
Lyapunov functions are essential tools in dynamical systems, as they allow the stability analysis of equilibrium points without the need to explicitly solve the system's equations. Despite their importance, no systematic method exists for…
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…
I give a brief overview of the resolution of the apparent problem of reconciling time symmetric microscopic dynamic with time asymmetric equations describing the evolution of macroscopic variables. I then show how the large deviation…
In this paper an autonomous analytical system of ordinary differential equations is considered. For an asymptotically stable steady state x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when…
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…
In this paper, we consider linear switched systems $\dot x(t)=A_{u(t)} x(t)$, $x\in\R^n$, $u\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\bf UAS} for short). We first…
Quadratic Lyapunov functions are prevalent in stability analysis of linear consensus systems. In this paper we show that weighted sums of convex functions of the different coordinates are Lyapunov functions for irreducible consensus…
Lur'e-type nonlinear systems are virtually ubiquitous in applied control theory, which explains the great interest they have attracted throughout the years. The purpose of this paper is to propose conditions to assess incremental asymptotic…
In this paper a first order analytical system of difference equations is considered. For an asymptotically stable fixed point x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when the matrix…
We consider group-valued cocycles over dynamical systems. The base system is a homeomorphism $f$ of a metric space satisfying a closing property, for example a hyperbolic dynamical system or a subshift of finite type. The cocycle $A$ takes…
We propose a moving horizon estimation scheme for joint state and parameter estimation for nonlinear uncertain discrete-time systems. We establish robust exponential convergence of the combined estimation error subject to process…
Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…
We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…
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…
We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function…
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…
While global convergence of the Douglas-Rachford iteration is often observed in applications, proving it is still limited to convex and a handful of other special cases. Lyapunov functions for difference inclusions provide not only global…
In 1986 Ya.V. Tatarinov presented the foundations of the theory of weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. It is assumed that for zero value of this…
Motivated by recent applications of the Lyapunov's method in artificial neural networks, which could be considered as dynamical systems for which the convergence of the system trajectories to equilibrium states is a necessity. We re-look at…
We derive converse Lyapunov theorems for input-to-state stability (ISS) of linear infinite-dimensional analytic systems. We show that input-to-state stability of a linear system does not imply existence of a coercive quadratic ISS Lyapunov…