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Firstly, a piecewise linear system is constructed through piecewise linearization of the Chinese high-speed train's nonlinear dynamics.
In [12], 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 [10].
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 [16] 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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