Topic
Piecewise linear function
About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.
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TL;DR: The effectiveness of the proposed approach to stability analysis of continuous-time piecewise affine systems is shown by analyzing an opinion dynamics model and two saturating control systems.
39 citations
TL;DR: A new and efficient method to calculate the line-of-action of a muscle as it wraps over bones and other tissues on its way from origin to insertion that is computationally efficient even for large numbers of cross sections.
Abstract: This paper presents a new and efficient method to calculate the line-of-action of a muscle as it wraps over bones and other tissues on its way from origin to insertion. The muscle is assumed to be a one-dimensional, massless, taut string, and the surfaces of bones that the muscle may wrap around are approximated by cross-sectional boundaries obtained by slicing geometrical models of bones. Each cross-sectional boundary is approximated by a series of connected line segments. Thus, the muscle path to be calculated is piecewise linear with vertices being the contact points on the cross-sectional boundaries of the bones. Any level of geometric accuracy can be obtained by increasing the number of cross sections and the number of line segments in each cross section. The algorithm is computationally efficient even for large numbers of cross sections.
39 citations
TL;DR: Many structured large scale linear programming problems can be transformed into an equivalent problem of maximizing a piecewise linear, concave function subject to linear constraints, yielding refinements of existing algorithms.
Abstract: Many structured large scale linear programming problems can be transformed into an equivalent problem of maximizing a piecewise linear, concave function subject to linear constraints. The concave problem can be solved in a finite number of steps using a steepest ascent algorithm. This principle is applied to block diagonal systems yielding refinements of existing algorithms. An application to the multistage problem yields an entirely new algorithm.
39 citations
TL;DR: A group of triangulation methods is introduced which includes the l1 and l2 norm methods of Dyn and Levin and Rippa as special cases and the results of several numerical experiments are presented.
39 citations
TL;DR: An explicit and exact stability test for planar systems is derived, which is given in terms of coefficients of transfer functions of subsystems, which drives a necessary stability condition and a sufficient stability condition for higher-order and bimodal systems.
39 citations