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Dynamical behaviours of an Euler discretized sliding mode control systems

Qu, Shaocheng and Xia, Xiaohua and Zhang, Jiangfeng (2014) Dynamical behaviours of an Euler discretized sliding mode control systems. IEEE Transactions on Automatic Control, 59 (9). pp. 2525-2529. ISSN 0018-9286

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The dynamical behaviors of an Euler discretized sliding mode control (SMC) systems based on equivalent control strategy are studied. A periodic-2 orbit in steady state is found for the switching function of the Euler discretized SMC systems. The time steps for the switching function to converge toward the periodic-2 orbit are obtained. When the discretized SMC system is stable, it further shows that the system states of the SMC systems will also enter into some periodic-2 orbits, and these periodic-2 orbits are characterized by explicit analytic expressions. Finally, simulation examples are given to illustrate the theoretical results.