An LMI based controller design method for a discrete-time linear system with time-varying state delays
An LMI based controller design method for a discrete-time linear system with time-varying state delays
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基于LMI的时变状态延迟离散时间线性系统控制器设计方法
DOI：
10.1093/imamci/dnv052
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发表时间：
2016
影响因子：
1.5
通讯作者：
Katsuya Satoh， Masami Saeki
中科院分区：
文献类型：
--
作者：
Nobutaka Wada;Katsuya Satoh， Masami Saeki
针对一类具有时变时滞的离散线性系统，给出了一种反馈控制器的设计方法。基于广义Lyapunov-Krasovskii函数推导出了所提出的设计条件。首先，一个设计条件推导出一个双线性矩阵不等式（BMI）条件。由于很难得到一个解决方案，满足BMI条件直接，我们转换的条件，以一个更容易处理的设计条件，通过引入一个松弛变量，具有特殊的结构。当标量参数固定时，所得到的条件可化为线性矩阵不等式条件。两个数值算例表明了该方法的有效性。
In this paper, we show a design method of a feedback controller for a discrete-time linear system with time-varying state delays. The proposed design condition is derived based on the generalized Lyapunov–Krasovskii function. Firstly, a design condition is derived as a bilinear matrix inequality (BMI) condition. Since it is difficult to obtain a solution that satisfies the BMI condition directly, we convert the condition to a more tractable design condition by introducing a slack variable that has a special structure. The obtained condition can be reduced to a linear matrix inequality condition when a scalar parameter is fixed. Two numerical examples are provided to show effectiveness of the proposed method.