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On the stabilization of nonlinear systems
1982 21st IEEE Conference on Decision and Control, 1982The so called Q-parametrization theorem for linear systems states that for a stable plant P, a compensator F yields a stable closed loop if and only if \(F=Q(I-PQ)^{-1}\) for some stable Q. In this paper the Q- parametrization theorem is extended to nonlinear systems.
Venkat Anantharam, Charles A. Desoer
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On robustness of nonlinear systems
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1998AbstractWe study the problem of measuring the robustness of stability for a perturbed discrete time nonlinear system. Various stability radii are introduced and their values for the nonlinear system and its linearization are compared. For the time‐invariant case the nonlinear and the linear version of the stability radius coincide generically.
Fabian Wirth, A.D.B. Paice
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On the Identification of Nonlinear Systems
IFAC Proceedings Volumes, 1982Abstract For the identification of systems in which the nonlinear element is in the feedback path, a new technique based on the Volterra characterisation of nonlinear system, is presented. The method is shown to have distinct computational advantages. Simulation studies using the proposed method are given.
N.C. Jagan, D.C. Reddy
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A nonlinear philosophy for nonlinear systems
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002A framework for system analysis and design is described based on nonlinear system models and nonperiodic signals generated by nonlinear systems. The proposed approach to analysis of nonlinear systems is based on an excitability index-a nonlinear counterpart of the magnitude frequency response of linear systems.
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Filtering by nonlinear systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.
J. Urías +2 more
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Factorization of Nonlinear Systems
1991We introduce a new concept of factor distribution for a nonlinear system as anew tool for studying the decomposition of such a system. The idea of factorizing generalizes a similar idea from linear system theory as well as the notion of controlled invariance for nonlinear systems.
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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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IEEE Transactions on Automatic Control, 1976
A dither is a high-frequency signal introduced into a nonlinear system with the object of augmenting stability. In this paper,[1] it is shown that the effects of dither depend on its amplitude distribution function. The stability of a dithered system is related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the ...
George Zames, N. Shneydor
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A dither is a high-frequency signal introduced into a nonlinear system with the object of augmenting stability. In this paper,[1] it is shown that the effects of dither depend on its amplitude distribution function. The stability of a dithered system is related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the ...
George Zames, N. Shneydor
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On the instability of nonlinear systems
IEEE Transactions on Automatic Control, 1973An extension of a well-known instability criterion is presented. The extension is considerably more powerful than the original result.
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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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