Related papers: Analysis of Periodic Feedback Shift Registers
This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
The Quasi Steady-State (QSS) model of long-term dynamics relies on the idea of time-scale decomposition. Assuming that the fast variables are infinitely fast and are stable in the long-term, the QSS model replaces the differential equations…
Time-series forecasting is a critical challenge in various domains and has witnessed substantial progress in recent years. Many real-life scenarios, such as public health, economics, and social applications, involve feedback loops where…
We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state…
In Floquet engineering, periodic driving is used to realize novel phases of matter which are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe of obtaining a static effective Hamiltonian.…
It is shown that a spin system with long range interactions can be converted into a chaotic dynamical system that is differentiable and low-dimensional. The thermodynamic limit of the spin system is then equivalent to studying the long term…
Large-scale simulations of the spin dynamics in quantum dots subjected to trains of periodic laser pulses enable us to describe and understand related experiments. By comparing the data for different models to experimental results, we gain…
We experimentally observe Floquet Raman transitions in the weakly driven solid state spin system of nitrogen-vacancy center in diamond. The periodically driven spin system simulates a two-band Wannier-Stark ladder model, and allows us to…
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…
Some recent papers have extended the concept of finite-time stability (FTS) to the context of 2D linear systems, where it has been referred to as finite-region stability (FRS). FRS methodologies make even more sense than the classical FTS…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
We consider linear dynamical systems under floating-point rounding. In these systems, a matrix is repeatedly applied to a vector, but the numbers are rounded into floating-point representation after each step (i.e., stored as a…
Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we…
The theoretical treatment of quasi-periodically driven quantum systems is complicated by the inapplicability of the Floquet theorem, which requires strict periodicity. In this work we consider a quantum system driven by a bi-harmonic…
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…
This paper presents a technique for designing output feedback controllers for constrained linear parameter-varying systems that are subject to persistent disturbances. Specifically, we develop an incremental parameter-varying output…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical…