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Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the Schrodinger equation. For a class of…
We show that quantum mechanical entanglement can prevail even in noisy open quantum systems at high temperature and far from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number N of…
A symmetry-preserving, reduced-order state observer is presented for the unmeasured part of a system's state, where the nonlinear system dynamics exhibit symmetry under the action of a Lie group. Leveraging this symmetry with a moving…
This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any position term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter,…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, \textit{i.e.} the states whose weights in the stationary distributions can be bounded away from $0$ as…
We show that a simple experimental setting of a locally pumped and lossy array of two-level quantum systems can stabilize states with strong long-range coherence. Indeed, by explicit analytic construction, we show there is an extensive set…
In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system…
We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
Power electronic devices such as HVDC and FACTS can be used to improve the damping of poorly damped inter-area modes in large power systems. This involves the use of wide-area feedback signals, which are transmitted via communication…
In this paper, we deal with the problem of the stabilization in the sample-and-hold sense, by emulation of continuous-time, observer-based, global stabilizers. Fully nonlinear time-delay systems are studied. Sufficient conditions are…
The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…