Related papers: Lyapunov Criterion for Stochastic Systems and Its …
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…
We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…
This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. We show that solutions…
Asynchronous-parallel algorithms have the potential to vastly speed up algorithms by eliminating costly synchronization. However, our understanding to these algorithms is limited because the current convergence of asynchronous (block)…
There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
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 show that the robust forward completeness for distributed parameter systems is equivalent to the existence of a corresponding Lyapunov function that increases at most exponentially along the trajectories.
This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate…
This paper investigates the mean stability of a class of discrete-time stochastic switched linear systems using the $L^p$-norm joint spectral radius of the probability distributions governing the switched systems. First we prove a converse…
We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
We consider a network of agents whose objective is for the aggregate of their states to converge to a solution of a linear program in standard form. Each agent has limited information about the problem data and can communicate with other…
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…
In this paper, we propose a distributed model predictive control (DMPC) scheme for linear time-invariant constrained systems which admit a separable structure. To exploit the merits of distributed computation algorithms, the stabilizing…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…
Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in analytic or numerically efficient methods for computing…