Finite Dimensional Filters for a Class of Nonlinear Systems and Immersion in a Linear System

1987 ◽  
Vol 25 (6) ◽  
pp. 1430-1439 ◽  
Author(s):  
J. Levine
Keyword(s):  
Nonlinear Systems ◽  
Linear System ◽  
Finite Dimensional

Finite-Dimensional Filtering and Control for Continuous-Time Nonlinear Systems

2004 ◽  
Vol 22 (2) ◽  
pp. 499-505
Author(s):  
Robert J. Elliott ◽  
Lakhdar Aggoun ◽  
Ali Benmerzouga
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Finite Dimensional ◽  
And Control

Minimum Rank Generalized Subspace Updating Approach for Nonlinear Systems

2005 ◽  
Author(s):  
Kiran D’Souza ◽  
Bogdan I. Epureanu
Keyword(s):  
Perturbation Theory ◽  
Nonlinear Systems ◽  
Linear System ◽  
Random Noise ◽  
Numerical Data ◽  
Truss Structures ◽  
Minimum Rank ◽  
Damage Scenarios ◽  
System A ◽  
Analysis Technique

An algorithm for analyzing a nonlinear system as an augmented linear system is presented. The method uses a nonlinear discrete model of the system and the form of the nonlinearities to create an augmented linear model of the system. A linear modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the augmented linear system after the onset of damage. Due to the specialized form of the augmentation, nonlinear damage causes asymmetric damage in the updated matrices. A generalized minimum rank perturbation theory, which requires knowledge of both right and left eigenvectors, is developed to handle the asymmetric damage scenarios. The damage extent algorithm becomes an iterative process when an incomplete set of right eigenvectors are known. The method is demonstrated using numerical data from nonlinear 3-bay truss structures. Various damage scenarios of the nonlinear systems are used to demonstrate the effectiveness of the augmentation and the generalized minimum rank perturbation theory, and the effect of random noise on the technique. The nonlinearities included in the 3-bay truss are cubic springs.

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. 

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.

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.

Formulation of Stochastic Linearization for Symmetric or Asymmetric M.D.O.F. Nonlinear Systems

1980 ◽  
Vol 47 (1) ◽  
pp. 209-211 ◽  
Author(s):  
P-T. D. Spanos
Keyword(s):  
Nonlinear Systems ◽  
Linear System ◽  
Solution Procedure ◽  
Stationary System ◽  
System Response ◽  
Equivalent Linear ◽  
Stochastic Linearization ◽  
Equivalent Linear System

A formulation of the method of stochastic linearization so that it is applicable for symmetric or asymmetric nonlinear systems is presented. Formulas for the generation of the equivalent linear system are given. The solution procedure for determining nonstationary or stationary system response statistics is outlined.

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