# piecewise linear system

## piecewise linear system

[′pēs‚wīz ¦lin·ē·ər ‚sis·təm]
(control systems)
A system for which one can divide the range of values of input quantities into a finite number of intervals such that the output quantity is a linear function of the input quantity within each of these intervals.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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References in periodicals archive ?
Firstly, a piecewise linear system is constructed through piecewise linearization of the Chinese high-speed train's nonlinear dynamics.
In , a research on a piecewise linear system without damping was made, and the closed-form solution for periodic response was obtained.
For instance, the stability and performance of a piecewise linear system were discussed by means of the quadratic and piecewise-quadratic Lyapunov functions which could cast as convex optimization problems and linear matrix inequalities (LMI) by Hassibi and Boyd .
By using this method, the piecewise linear system can be transformed into a hybrid logic dynamical system [28, 29].
In practical systems, the piecewise linear system is an efficient method to approximate nonlinear system.
Consider the piecewise linear system (86) with u [equivalent to] 0.
have established an approach to generate multiscroll attractors via destabilization of piecewise linear systems based on Hurwitz matrix.
Nicol, "Generation of multi-scroll attractors without equilibria via piecewise linear systems," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.
Yang, "On the number of limit cycles in general planar piecewise linear systems of node-node types," Journal of Mathematical Analysis and Applications, vol.
Schwarz, "Linear conjugacy of n-dimensional piecewise linear systems," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.
Thus, results similar to those of our model can be obtained in the study of other continuous piecewise linear systems.
A closely related work is the stability analysis of piecewise linear systems by  in which piecewise quadratic Lyapunov functions were constructed using convex optimization in terms of linear matrix inequalities (LMIs) as an alternative to a globally quadratic Lyapunov function.

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