Abstract This paper proposes a stability criterion for linear systems with multi-rate sampled data by constructing novel Lyapunov functionals. The systems are represented as linear systems with input delay. The Lyapunov functionals consist of a quadratic function, an integral term related to the sampling intervals of each sensor and looped-functionals related to the sampling intervals of whole systems. In the view of the Lyapunov stability theorem, the quadratic function and the integral term require the positivity condition, whereas the looped-functionals do not require the positivity condition because the functionals are zeros at the sampling instants. Furthermore, the looped-functionals exploit the information on the sampled state and the state at the next sampling instants. Based on the Lyapunov functionals, this paper derives a stability criterion in terms of linear matrix inequalities. The simulation results show the effectiveness of the proposed stability criterion.

中文翻译：

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多速率采样数据线性系统的改进稳定性判据

摘要 本文通过构造新的李雅普诺夫泛函，提出了多速率采样数据线性系统的稳定性判据。这些系统被表示为具有输入延迟的线性系统。Lyapunov 泛函由二次函数、与每个传感器的采样间隔相关的积分项和与整个系统的采样间隔相关的循环泛函组成。根据李雅普诺夫稳定性定理，二次函数和积分项需要正条件，而环泛函不需要正条件，因为泛函在采样时刻为零。此外，循环函数利用关于采样状态和下一个采样时刻的状态的信息。基于李雅普诺夫泛函，本文根据线性矩阵不等式推导出稳定性判据。仿真结果表明了所提出的稳定性准则的有效性。