An LMI-based controller design method for a discrete-time linear system with time-varying state delays

Wada Nobutaka; Satoh Katsuya; Saeki Masami

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An LMI-based controller design method for a discrete-time linear system with time-varying state delays

机译：基于LMI的控制器设计方法，用于带有时变状态延迟的离散时间线性系统

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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.

机译：在本文中，我们示出了具有时变状态延迟的离散时间线性系统的反馈控制器的设计方法。基于广义Lyapunov-Krasovskii函数导出所提出的设计条件。首先，设计条件作为双线性矩阵不等式（BMI）条件导出。由于难以直接获得满足BMI条件的解决方案，因此我们通过引入具有特殊结构的松弛变量来将条件转换为更易无设计状态。当标量参数固定时，可以将所获得的条件降低到线性矩阵不等式状态。提供了两个数值例子以显示所提出的方法的有效性。

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来源
《IMA Journal of Mathematical Control and Information》 |2017年第2期|共20页
作者
Wada Nobutaka; Satoh Katsuya; Saeki Masami;
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作者单位

Hiroshima Univ Div Mech Syst &

Appl Mech 1-4-1 Kagamiyama Higashihiroshima 7398527 Japan;

Hiroshima Univ Div Mech Syst &

Appl Mech 1-4-1 Kagamiyama Higashihiroshima 7398527 Japan;

Hiroshima Univ Div Mech Syst &

Appl Mech 1-4-1 Kagamiyama Higashihiroshima 7398527 Japan;

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原文格式 PDF
正文语种 eng
中图分类控制论、信息论（数学理论）;
关键词
time-varying delay; feedback control; Lyapunov-Krasovskii function; LMI;

机译：时变延迟;反馈控制;Lyapunov-Krasovskii功能;LMI;

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1. An LMI-based controller design method for a discrete-time linear system with time-varying state delays [J] . Wada Nobutaka, Satoh Katsuya, Saeki Masami IMA Journal of Mathematical Control and Information . 2017,第2期

机译：基于LMI的控制器设计方法，用于带有时变状态延迟的离散时间线性系统
2. Robust global controller design for discrete-time descriptor systems with multiple time-varying delays [J] . Mobayen Saleh, Bayat Farhad, Omidvar Hossein, International Journal of Robust and Nonlinear Control . 2020,第7期

机译：具有多个时变延迟的离散时间描述符系统的强大全局控制器设计
3. An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique [J] . Mobayen Saleh Nonlinear dynamics . 2015,第1a2期

机译：基于LMI的鲁棒跟踪器，使用最优复合非线性反馈技术，针对具有多个时变时滞的不确定线性系统
4. H/sub /spl infin// controller design for discrete-time linear systems with time-varying delays in state [C] . Ki Tae Kim, Sang Hyun Cho, Joon Ki Kim . 2001

机译：H / sub / spl infin //用于状态随时间变化的离散时间线性系统的控制器设计
5. Design of controllers for nonlinear electrohydraulic systems with time delays. [D] . Ge, Jianlin. 1992

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An LMI-based controller design method for a discrete-time linear system with time-varying state delays

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