Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy Noise

Li, Wenrui and Fei, Weiyin and Liang, Yong and Mao, Xuerong (2023) Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy Noise. IMA Journal of Mathematical Control and Information, 40 (2). pp. 232-252. ISSN 0265-0754 (https://doi.org/10.1093/imamci/dnad008)

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Abstract

We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise.

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