scholarly journals Stochastic linearization of nonlinear point dissipative systems

2004 ◽  
Vol 2004 (65) ◽  
pp. 3541-3563
Author(s):  
James A. Reneke
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Dissipative Systems ◽  
Input Output ◽  
Operator Representation ◽  
Covariance Kernel ◽  
Finite Dimensional ◽  
Convergence Results ◽  
Stochastic Linearization ◽  
Output Operator

Stochastic linearization produces a linear system with the same covariance kernel as the original nonlinear system. The method passes from factorization of finite-dimensional covariance kernels through convergence results to the final input/output operator representation of the linear system.

scholarly journals Positive Normalization of Discrete Descriptor System under Disturbance

MATEMATIKA ◽  
2018 ◽  
Vol 34 (3) ◽  
pp. 141-147
Author(s):  
Ahmad Iqbal Baqi ◽  
Admi Nazra ◽  
Zulakmal Zulakmal ◽  
Lyra Yulianti ◽  
Muhafzan Muhafzan
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Unique Solution ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Real Problem ◽  
Sufficient Condition ◽  
Input Output ◽  
Application Field

It is well known the descriptor systems have a wide application field. Usually it appear as a mathematical model of a real problem, mainly the model that involves the input output relationship. It is well known that a descriptor linear system has an unique solution if the pencil matrix of the system is regular. However, there are some systems that are not regular. Moreover, even though the system is regular the solution can contain the noncausal behavior. Therefore, it is necessary to normalize the descriptor system so as it has well behavior. In this paper, we propose a feedback to normalize a discrete descriptor system under disturbance. Furthermore, we establish a sufficient condition in order for the discrete descriptor system under disturbance can be normalized positively.

scholarly journals Feedback stabilization of one-dimensional parabolic systems related to formations

2015 ◽  
Vol 63 (1) ◽  
pp. 295-303
Author(s):  
H. Sano
Keyword(s):  
Finite Dimension ◽  
Time Derivative ◽  
Parabolic Systems ◽  
Feedback Stabilization ◽  
Boundary Values ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Neumann Type ◽  
Sturm Liouville ◽  
Output Operator

Abstract This paper is concerned with the problem of stabilizing one-dimensional parabolic systems related to formations by using finitedimensional controllers of a modal type. The parabolic system is described by a Sturm-Liouville operator, and the boundary condition is different from any of Dirichlet type, Neumann type, and Robin type, since it contains the time derivative of boundary values. In this paper, it is shown that the system is formulated as an evolution equation with unbounded output operator in a Hilbert space, and further that it is stabilized by using an RMF (residual mode filter)-based controller which is of finite-dimension. A numerical simulation result is also given to demonstrate the validity of the finite-dimensional controller

ANALYTICAL SOLUTIONS OF SYSTEMS WITH PIECEWISE LINEAR DYNAMICS

2010 ◽  
Vol 20 (02) ◽  
pp. 509-518 ◽  
Author(s):  
Y. KOMINIS ◽  
T. BOUNTIS
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Piecewise Linear ◽  
Time Intervals ◽  
Linear Dynamics ◽  
Piecewise Linear System ◽  
Nonautonomous Dynamical Systems ◽  
Autonomous Component ◽  
Physical Phenomena ◽  
Linear Periodic System

A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.

Dynamics of Oscillator With Soft Impacts

2001 ◽  
Author(s):  
František Peterka
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Mechanical System ◽  
Linear Model ◽  
Piecewise Linear ◽  
Impact Oscillator ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
New Phenomena ◽  
The Impact

Abstract The impact oscillator is the simplest mechanical system with one degree of freedom, the periodically excited mass of which can impact on the stop. The aim of this paper is to explain the dynamics of the system, when the stiffness of the stop changes from zero to infinity. It corresponds to the transition from the linear system into strongly nonlinear system with rigid impacts. The Kelvin-Voigt and piecewise linear model of soft impact was chosen for the study. New phenomena in the dynamics of motion with soft impacts in comparison with known dynamics of motion with rigid impacts are introduced in this paper.

scholarly journals Identification of Nonlinear Systems: Volterra Series Simplification

10.14311/976 ◽  
2007 ◽  
Vol 47 (4-5) ◽  
Author(s):  
A. Novák
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Transfer Function ◽  
Linear System ◽  
Impulse Response ◽  
Volterra Series ◽  
Series Representation ◽  
Multimedia Systems ◽  
Audio Amplifier ◽  
Enormous Number

Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown. 

Input Requirements and Parametric Errors for System Identification Under Periodic Excitation

1972 ◽  
Vol 94 (4) ◽  
pp. 296-302 ◽  
Author(s):  
L. L. Hoberock ◽  
G. W. Stewart
Keyword(s):  
Linear System ◽  
Input State ◽  
Matrix Elements ◽  
Periodic Excitation ◽  
Input Output ◽  
Input Matrix ◽  
Multiple Input ◽  
Minimum Number ◽  
Single Input ◽  
Work Done

This paper provides the conditions on periodic system excitation necessary for unique identification using a multiple input state model of a dynamic system. Results include the minimum number of input frequencies necessary to uniquely determine all state and input matrix elements of an n dimensional linear system. It is shown that this development encompasses earlier work done on single input-output systems. A technique is provided for predicting parametric errors to be expected from identification under periodic excitation, and several examples are used to illustrate these errors.

scholarly journals THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED

2019 ◽  
Vol 7 ◽  
Author(s):  
WILLIAM SLOFSTRA
Keyword(s):  
Hilbert Space ◽  
Linear System ◽  
Tensor Product ◽  
Quantum Correlations ◽  
Embedding Theorem ◽  
Product Strategy ◽  
Finite Dimensional ◽  
Universal Embedding ◽  
Quantum Strategies ◽  
Finite Dimensional Hilbert Space

We construct a linear system nonlocal game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product strategy. In particular, this shows that the set of (tensor-product) quantum correlations is not closed. The constructed nonlocal game provides another counterexample to the ‘middle’ Tsirelson problem, with a shorter proof than our previous paper (though at the loss of the universal embedding theorem). We also show that it is undecidable to determine if a linear system game can be played perfectly with a finite-dimensional strategy, or a limit of finite-dimensional quantum strategies.

A Practical Technique for Spectral Analysis of Nonlinear Systems Under Stochastic Parametric and External Excitations

1991 ◽  
Vol 113 (4) ◽  
pp. 516-522 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Spectral Response ◽  
Duffing Oscillator ◽  
Gaussian White Noise ◽  
Matching Condition ◽  
External Noise ◽  
Equivalent Linearization ◽  
Parametric Noise ◽  
Parametric And External Excitations

A practical approach is developed for analyzing the spectral response of a nonlinear system subjected to both parametric and external Gaussian white noise excitations. The technique is implemented through the combined methods of equivalent external excitation and equivalent linearization to derive an equivalent linear system under equivalent external noise excitation. The spectral response is then obtained through utilizing the input/output spectral relation and covariance matching condition. A parametric noise excited linear system, Duffing oscillator, and nonlinear system with hysteretic nonlinearity are selected for investigation. The validity of the proposed method for analyzing spectral response is further supported by some analytical solutions and FFT technique through Monte Carlo simulations.

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