By Domine Leenaerts, Wim M.G. van Bokhoven
ISBN-10: 144195046X
ISBN-13: 9781441950468
ISBN-10: 1475761902
ISBN-13: 9781475761900
Piecewise Linear (PL) approximation of non-linear behaviour is a well known procedure in synthesis and research of electric networks. notwithstanding, the PL description might be effective in facts garage and the outline may still let easy retrieval of the kept info. moreover, it'd be necessary if the version description might deal with a wide category of piecewise linear mappings.
Piecewise Linear Modeling and Analysis explains intimately all attainable version descriptions for successfully storing piecewise linear features, beginning with the Chua descriptions. specific rationalization on how the version parameter could be got for a given mapping is equipped and verified by way of examples. The types are ranked to check them and to teach which version can deal with the biggest classification of PL mappings.
All version descriptions are implicitly concerning the Linear Complementarity challenge and such a lot resolution innovations for this challenge, like Katzenelson and Lemke, are mentioned based on examples which are defined intimately.
To examine PL electric networks a simulator is essential. PiecewiseLinear Modeling and Analysis presents a close define of a potential PL simulator, together with pseudo-programming code. numerous simulation domain names like brief, AC and distortion are mentioned. The e-book explains the horny gains of PL simulators with appreciate to mixed-level and mixed-signal simulation whereas paying due regard additionally to hierarchical simulation.
Piecewise Linear Modeling and Analysis exhibits intimately what percentage latest elements in electric networks might be modeled. those variety from electronic common sense and analog uncomplicated components corresponding to transistors to complicated structures like Phase-Locked Loops and detection structures. Simulation effects also are supplied. The booklet concludes with a dialogue on how to define a number of recommendations for PL features or networks. back, the commonest concepts are defined utilizing transparent examples.
Piecewise Linear Modeling and Analysis is an necessary consultant for researchers and architects drawn to community concept, community synthesis and community analysis.
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Additional resources for Piecewise Linear Modeling and Analysis
Sample text
3. Obtaining the model parameters Up to now we have demonstrated that for a given continuous piecewise linear function it is possible to come up with an explicit piecewise linear model description under the condition that the LCP matrix is of class P. However, the first step is to come to the implicit PL model description of the given mapping. In this section we will explain how this model can be derived [15,16]. Assume that a general PL mapping is given as N segments (Ji i =1, ... ,N and for each segment • The linear mapping y = AiX+ Ii' Ai E Rmxn, Ii E R m • The boundaries of the segment described by Kix + Si 2:: 0, Ki E R kxn , S E Rk Let us consider the situation that two boundary planes intersect each other, thus forming four segments.
Consider again the situation in Fig. 4. For the two adjacent regions D and C with boundary H 2 the Jacobian matrix change must be equal to the matrix change for the two adjacent regions B and A. Thus the change of the matrix must be independent of where the crossing of boundary H 2 takes place. 12) j with k i the k-factors belonging to the PL hyperplanes and with k; constant for the crossing. 13) k; =k;+(3)(-1)~k; =-3 and thus the consistent variation property holds. It is now easy to obtain the complete function description for Fig.
46a) of the second order and so forth. 10. First and second order base functions 56 PIECEWISE LINEAR MODEL DESCRIPTIONS expression for the mapping R n ~ R m ; x ~ y . The explicit description just derived is more general than Kah because the higher order base functions allow a more complex geometry of the domain space in dimensions higher than R2. In that sense it is an extension to the known explicit model descriptions. On the other hand it is not the most general explicit form because of the assumption that the matrix D is lower triangular.