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We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
This study examines the discharge behaviour of a cylindrical LiFeS2 cell to evaluate the parameters that can be used to predict and estimate the nonlinear dynamic response of a battery. A linear model is developed to simulate the discharge…
We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed…
Nonlinear oscillators are commonly encountered in a wide range of physical and engineering systems, exhibiting rich and complex dynamics. Among these, the Van der Pol oscillator is well known for its self-sustained limit cycle behavior.…
In this article, we detail the design of an output feedback stabilizing control law for an underactuated network of N subsystems of n + m heterodirectional linear first-order hyperbolic Partial Differential Equations interconnected through…
In this book chapter we analyze the high excitation nonlinear response of the Jaynes-Cummings model in quantum optics when the qubit and cavity are strongly coupled. We focus on the parameter ranges appropriate for transmon qubits in the…
For the study of chaotic dynamics and dimension of attractors the concepts of the Lyapunov exponents was found useful and became widely spread. Such characteristics of chaotic behavior, as the Lyapunov dimension and the entropy rate, can be…
The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback…
Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…
The problem of partial stabilization for nonlinear control systems described by the Ito stochastic differential equations is considered. For these systems, we propose a constructive control design method which leads to establishing the…
Non-universal dynamics is shown to occur in a one-dimensional non-equilibrium system of hard-core particles. The stochastic processes included are pair creation and annihilation (with rates e and e') and symmetric hopping rates which…
The Hubbard model is a prototype for strongly correlated electrons in condensed matter, for molecules and fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the excitation…
We conduct a theoretical study of the nonlinear optical response of a two-dimensional semi-conductor quantum dot supercrystal subjected to a quasi-resonant continuous wave excitation. Aconstituent quantum dot is odeled as a three-level…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
We present an analysis of a system of weakly coupled Hubbard chains based on combining an exact study of spectral functions of the uncoupled chain system with a renormalization group method for the coupled chains. For low values of the…
A new network data transmission strategy was proposed in Zhang \& Chen [2005] (arXiv:1405.2404), where the resulting nonlinear system was analyzed and the effectiveness of the transmission strategy was demonstrated via simulations. In this…
Since the classical proportional-integral-derivative (PID) controller has continued to be the most widely used feedback methods in engineering systems by far, it is crucial to investigate the working mechanism of PID in dealing with…
In this letter we study how hyperbolic and non hyperbolic regions in the neighborhood of a resonant island perform a important role allowing or forbidding stickiness phenomenon around islands in conservative systems. The vicinity of the…