Related papers: An example on Lyapunov stability and linearization
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
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…
This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…
For linear periodic finite-dimensional systems, it is well-known that, first, exponential stability is equivalent to the existence of a unique periodic positive definite solution to the Lyapunov equation, and second, the Lyapunov equation…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set and its switching rates at current time depend on the…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
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…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without non-constant motions which have the equilibrium as limit…
We investigate discret conditions for stability and asymptotic stability by Lyapunov and the point of equilibrium of autonomous system of differential equations.
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
We present an example of a discontinuity point for the Lyapunov exponents when viewed as a function of the cocycle in a topology finer than the $C^0$-topology. The linear cocycle taking values in SL(2,R) is locally constant, defined over a…