Article
Finding All DC Operating Points of PiecewiseLinear Circuits Containing Neither Voltage nor Current Controlled Resistors
01/2005; DOI: 10.1093/ietfec/e88a.6.1631
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Conference Paper: Finding all solutions of piecewiselinear resistive circuits using the dual simplex method
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ABSTRACT: An efficient algorithm is proposed for finding all solutions of piecewiselinear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed in to an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficientCircuits and Systems, 2000. Proceedings. ISCAS 2000 Geneva. The 2000 IEEE International Symposium on; 02/2000  [Show abstract] [Hide abstract]
ABSTRACT: An important application of complementarity theory consists in solving sets of piecewiselinear equations and hence in the analysis of piecewiselinear resistive circuits. The authors show how a generalized version of the linear complementarity problem can be used to analyze a broad class of piecewiselinear circuits. Nonlinear resistors that are neither voltage nor current controlled can be allowed, and no restrictions on the linear part of the circuit have to be made. As a second contribution, the authors describe an algorithm for the solution of the generalized complementarity problem and show how it can be applied to yield a complete description of the DC solution set as well as of drivingpoint and transfer characteristicsIEEE Transactions on Circuits and Systems 12/1989;  Mathematical concepts and techniques for modelling of staticand dynamicsystems..
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