Related papers: Necessary and Sufficient Conditions for Stable Syn…
This note studies (practical) asymptotic stability of nonlinear networked control systems whose protocols are not necessarily uniformly globally exponentially stable. In particular, we propose a Lyapunov-based approach to establish…
We consider the time-dependent nonlinear system $\dot q(t)=u(t)X(q(t))+(1-u(t))Y(q(t))$, where $q\in\R^2$, $X$ and $Y$ are two %$C^\infty$ smooth vector fields, globally asymptotically stable at the origin and $u:[0,\infty)\to\{0,1\}$ is an…
We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization…
We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is motivated by the desire to characterize local dynamical…
The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized…
For a strictly stationary sequence of random vectors in $\mathbb{R}^d$ we study convergence of partial sum processes to L\'evy stable process in the Skorohod space with $J_1$-topology. We identify necessary and sufficient conditions for…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…
We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies…
We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
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…
In the context of mechanical Lagrangian dynamics, we prove a new Lyapunov instability criterion for a non strict local minimum equilibrium point of a smooth potential where the sufficient condition for instability is the existence of a…
It has been shown by Le Jan that, given a memoryless-noise random dynamical system together with an ergodic distribution for the associated Markov transition probabilities, if the support of the ergodic distribution admits locally…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
For an underactuated (simple) Hamiltonian system with two degrees of freedom and one degree of underactuation, a rather general condition that ensures its stabilizability, by means of the existence of a (simple) Lyapunov function, was found…
We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
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…