Stabilization of hybrid systems by feedback control based on discrete-time state and mode observations

Lu, Jianqiu and Li, Yuyuan and Mao, Xuerong and Qiu, Qinwei (2017) Stabilization of hybrid systems by feedback control based on discrete-time state and mode observations. Asian Journal of Control. pp. 1-10. ISSN 1561-8625

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    Abstract

    Recently, Mao [1] proposed a kind of feedback control based on discrete time state observations to stabilize continuous-time hybrid stochastic systems in mean-square sense. We find that the feedback control there still depends on the continuous-time observations of the mode. However, it usually costs to identify the current mode of the system in practice. So we can further improve the control to reduce the control cost by identifying the mode at discrete times when we make observations for the state. In this paper, we aim to design such a type of feedback controls based on the discrete-time observations of both state and mode to stabilize the given unstable hybrid stochastic differential equations (SDEs) in the sense of mean-square exponential stability. Moreover, a numerical example is given to illustrate our results.