The domain of attraction of nonlinear functional difference systems is studied. A sufficient condition for determining the domain of attraction is given based on a non-negative parameter matrix whose spectral radius ...The domain of attraction of nonlinear functional difference systems is studied. A sufficient condition for determining the domain of attraction is given based on a non-negative parameter matrix whose spectral radius ρis less than one and on the characteristic space associated with ρ.展开更多
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has...The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.展开更多
The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is comp...The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.展开更多
This paper presents a novel Koopman Operator based framework to estimate the region of attraction for power system transient stability analysis.The Koopman eigenfunctions are used to numerically construct a Lyapunov f...This paper presents a novel Koopman Operator based framework to estimate the region of attraction for power system transient stability analysis.The Koopman eigenfunctions are used to numerically construct a Lyapunov function.Then the level set of the function is utilized to estimate the boundary of the region of attraction.The method provides a systematic method to construct the Lyapunov function with data sampled from the state space,which suits any power system models and is easy to use compared to traditional Lyapunov direct methods.In addition,the constructed Lyapunov function can capture the geometric properties of the region of attraction,thus providing useful information about the instability modes.The method has been verified by a simple illustrative example and three power system models,including a voltage source converter interfaced system to analyze the large signal synchronizing instability induced by the phase lock loop dynamics.The proposed method provides an alternative approach to understanding the geometric properties and estimating the boundary of the region of attraction of power systems in a data driven manner.Index Terms-Koopman operator,lyapunov function,power system transient stability,region of attraction.展开更多
This paper investigates the stability analysis and antiwindup design problem for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the swit...This paper investigates the stability analysis and antiwindup design problem for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the switched Lyapunov function approach. Supposing that a set of linear dynamic output controllers have been designed to stabilize the switched system without considering its input saturation, we design antiwindup compensation gains in order to enlarge the domain of attraction of the closed-loop system in the presence of saturation. Then, in terms of a sector condition, the antiwindup compensation gains which aim to maximize the estimation of domain of attraction of the closed-loop system are presented by solving a convex optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to demonstrate the effectiveness of the proposed design method.展开更多
文摘The domain of attraction of nonlinear functional difference systems is studied. A sufficient condition for determining the domain of attraction is given based on a non-negative parameter matrix whose spectral radius ρis less than one and on the characteristic space associated with ρ.
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.
文摘The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.
文摘The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.
基金supported by the National Key R&D Program of China Response-driven intelligent enhanced analysis and control for bulk power system stability(2021YFB2400800)。
文摘This paper presents a novel Koopman Operator based framework to estimate the region of attraction for power system transient stability analysis.The Koopman eigenfunctions are used to numerically construct a Lyapunov function.Then the level set of the function is utilized to estimate the boundary of the region of attraction.The method provides a systematic method to construct the Lyapunov function with data sampled from the state space,which suits any power system models and is easy to use compared to traditional Lyapunov direct methods.In addition,the constructed Lyapunov function can capture the geometric properties of the region of attraction,thus providing useful information about the instability modes.The method has been verified by a simple illustrative example and three power system models,including a voltage source converter interfaced system to analyze the large signal synchronizing instability induced by the phase lock loop dynamics.The proposed method provides an alternative approach to understanding the geometric properties and estimating the boundary of the region of attraction of power systems in a data driven manner.Index Terms-Koopman operator,lyapunov function,power system transient stability,region of attraction.
基金supported by the National Natural Science Foundation of China(Nos.61174073,90816028)
文摘This paper investigates the stability analysis and antiwindup design problem for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the switched Lyapunov function approach. Supposing that a set of linear dynamic output controllers have been designed to stabilize the switched system without considering its input saturation, we design antiwindup compensation gains in order to enlarge the domain of attraction of the closed-loop system in the presence of saturation. Then, in terms of a sector condition, the antiwindup compensation gains which aim to maximize the estimation of domain of attraction of the closed-loop system are presented by solving a convex optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to demonstrate the effectiveness of the proposed design method.
