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.