Results 221 to 230 of about 350,611 (269)
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Perturbations in Nonlinear Systems
SIAM Journal on Mathematical Analysis, 1972If a certain system of nonlinear differential equations has a bounded solution $x(t)$, then for the same system subject to a small perturbation the existence of a solution $y(t)$ which lies “close” to $x(t)$ is established.
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Annals of the New York Academy of Sciences, 1960
The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested ...
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The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested ...
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Journal of the Franklin Institute, 1989
Two nonlinear three-dimensional systems \((x(t),y(t),z(t))\), which exhibit chaotic characteristics are analyzed with the aid of computer graphics. The first system is represented by Lorenz model. The second system is represented by Chua's electric circuit model (double scroll system), which contains the nonlinear element.
Ku, Y. H., Sun, Xiaoguang
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Two nonlinear three-dimensional systems \((x(t),y(t),z(t))\), which exhibit chaotic characteristics are analyzed with the aid of computer graphics. The first system is represented by Lorenz model. The second system is represented by Chua's electric circuit model (double scroll system), which contains the nonlinear element.
Ku, Y. H., Sun, Xiaoguang
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The nonlinear-by-singularity systems
2008 15th IEEE International Conference on Electronics, Circuits and Systems, 2008The present work focuses on singularities, in terms of time functions, which are met in description of switching or sampling electronics systems, and on understanding of some basic nonlinear physical systems. The state-form dx/dt = [A(x,t)]x + [B(x,t)]u(t), and not the normal-form dx/dt = Phi(x,u,t), is preferred for use.
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Discrete nonlinear systems: on the admissible nonlinear disturbances
Journal of the Franklin Institute, 2001Consider the linear nominal discrete system \[ x_{i+1}= Ax_i,\quad y_i= Cx_i,\quad x_0\in \mathbb{R}^n\tag{1} \] and a perturbed form \[ x^\xi_{i+1}= Ax^\varepsilon_i+ Be_i+ g(\beta_i) f(x^\xi_i),\;x^\xi_0= x_0+ w,\;y^\xi_i= Cx^\xi_i,\tag{2} \] where \(e_i\), \(\beta_i\), \(w\) are some disturbance parameters. The disturbance \((w,(e_i),(\beta_i))\) is
Mostafa Rachik +3 more
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Identification of nonlinear LFR systems with two nonlinearities
2013 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2013When identifying a system (e.g. mechanical, electrical or chemical) based on inand output measurements and without physical knowledge, an engineer faces many choices. First of all, there exist standard linear models, but when those do not sufficiently well describe the data, nonlinear models should be considered.
Van Mulders, Anne, Vanbeylen, Laurent
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On System Gains, Nonlinearity Measures, and Linear Models for Nonlinear Systems
IEEE Transactions on Automatic Control, 2009This article is concerned with the assessment and derivation of (best) linear models for nonlinear systems. We introduce a general framework reminiscent of uncertainty descriptions in linear robust control theory in order to define a family of six model quality indices for linear models of nonlinear systems.
Tobias Schweickhardt, Frank Allgöwer
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Observability of Nonlinear Systems
IMA Journal of Mathematical Control and Information, 1984We consider the observability of systems of the form \(\dot x=Ax+Nx,y=Fx\), where A is a linear operator and N and F are nonlinear. We show that if the system is linearized about an equilibrium point \(x_ e\) and the linearized system is continuously initially observable, then the nonlinear system is continuously initially observable in some ...
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Nonlinear controllers for nonlinear systems with input nonlinearities
Proceedings of the 36th IEEE Conference on Decision and Control, 1999The authors consider control systems of the type \[ \dot x= f(x,\sigma(u)),\quad x(0)= x_0,\quad t\geq 0, \] where \(\sigma\) denotes an input nonlinearity -- in many cases saturation -- and present a methodology for designing globally stabilizing nonlinear controllers.
Haddad, Wassim M. +2 more
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The Behavior of Nonlinear Systems
Journal of the Aeronautical Sciences, 1956Many of the phenomena that occur in the world around us are governed by nonlinear relationships. In the development of the mathematical sciences, the difficulties of nonlinear analysis have hindered the formulation of nonlinear concepts that would permit us to understand such phenomena. In the present article, our progress in understanding the behavior
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