Related papers: Coordinate-invariant incremental Lyapunov function…
In this paper, we extend two classes of functions involved in asymptotic stability analyses. The goal of this extension is to study a maximization problem on the reachable values of a discrete-time dynamical system. This specific…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
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…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
From the analyticity properties of the equation governing infinitesimal perturbations, it is shown that all stability properties of spatially extended 1D systems can be derived from a single function that we call entropy potential since it…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
We study the entropy and Lyapunov exponents of invariant measures $\mu$ for smooth surface diffeomorphisms $f$, as functions of $(f,\mu)$. The main result is an inequality relating the discontinuities of these functions. One consequence is…
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…
It is known that Iterated Function Systems generated by orientation preserving homeomorphisms of the unit interval admit a unique invariant measure on $(0,1)$. The setup for this result is the positivity of Lyapunov exponents at both fixed…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
The stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as Lyapunov stability criteria. From the results obtained it follows that, unlike solitons, all the allowed compacton…
In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the…
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…
In this work, we study finite-time stability of switched and hybrid systems in the presence of unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of the system to be finite time stable.…
The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincar{\'e} inequality, the existence of some Lyapunov function and the exponential…
In 2019 Anthony Quas, Philippe Thieullen and Mohamed Zarrabi introduced the concept of strong fast invertibility for linear cocycles. It relates the growth of volumes between different initial times and, together with a condition on…
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.
The general theory of Lyapunov's stability of first-order differential inclusions in Hilbert spaces has been studied by the authors in a previous work. This new contribution focuses on the natural case when the maximally monotone operator…