Small-signal behavior of nonlinear lumped networks

Desoer, C.; Wong, K.K.

doi:10.1109/proc.1968.6134

Cited by 16 publications

(3 citation statements)

References 11 publications

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“…Popular general purpose simulation packages like SPICE (Nagels and Pederson, 1973) offer small signal analysis options based upon a linearization of the original system equations as used above. A theoretic foundation for this approach can be found in the paper of Desoer and Wong (1968), where it is shown that the solution of the linearized nonlinear system equations comes arbitrarily close to the small signal solution of the original nonlinear equations for excitations with an amplitude that tends to zero. The major condition to proof this result is that the second derivative of the nonlinear functions exist.…”

Section: Small Signal Analysismentioning

confidence: 99%

Structure discrimination in block-oriented models using linear approximations: A theoretic framework

et al. 2015

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In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints. The key idea is to monitor the movements of the poles and zeros of the linearized models and to reduce the number of candidate models on the basis of these observations.Besides the well known open loop single branch Wiener-, Hammerstein-, and Wiener-Hammerstein systems, we also cover a number of more general structures like parallel (multi branch) Wiener-Hammerstein models, and closed loop block oriented models, including linear fractional representation (LFR) models.

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Section: Small Signal Analysismentioning

confidence: 99%

Structure discrimination in block-oriented models using linear approximations: A theoretic framework

et al. 2015

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“…In addition, it may be shown that the peak absolute di erence between the solution dx of the approximate system (5 a) and the solution d x of the nonlinear system (3 a) is bounded, provided that the approximate system (5 a) is stable, d r is su ciently small and the initial conditions d x( 0) and dx(0) are zero (Desoer andWong 1968, Desoer andVidyasagar 1975, section 4.9). Once again, it is straightforward to extend this result to encompass non-zero initial conditions which are su ciently close to the origin.…”

Section: Gain-scheduled and Nonlinear Systems 291mentioning

confidence: 99%

Gain-scheduled and nonlinear systems: Dynamic analysis by velocity-based linearization families

Leith¹,

Leithead²

1998

International Journal of Control

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A family of velocity-based linearizations is proposed for a nonlinear system. In contrast to the conventional series expansion linearization, a member of the family of velocity-based linearizations is valid in the vicinity of any operating point, not just an equilibrium operating point. The velocity-based linearizations facilitate dynamic analysis far from the equilibrium operating points and enable the transient behaviour of the nonlinear system to be investigated. Using velocity-based linearizations, stability conditions are derived for both smooth and non-smooth nonlinear systems which avoid the restrictions to trajectories lying within an unnecessarily (perhaps excessively) small neighbourhood about the equilibrium operating points inherent in existing frozen-input theory. For systems where there is no restriction on the rate of variation the velocity-based linearization analysis is global in nature. The analysis techniques developed, although quite general, are motivated by the gain-scheduling design approach and have the potential for direct application to the analysis of gain-scheduled systems.

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“…Simplicity of T follows immediately from (1). Thus, T-'(TD)D is an operator, and (1) implies that (4) [IT-yx-T-yII <-b-llyl-y=ll for all Yl, Ye (TD) .M oreover, since 0D, (2)shows that T0 {0}. Hence, T-0=0 and (4) yields (5) IIT-y[I <-b-lllyll for all y (TD).…”

mentioning

confidence: 97%