连续综合控制系统的状态反馈广义<i>H</i><sub>2 </sub>控制

孙凤琪

doi:10.21656/1000-0887.420169

连续综合控制系统的状态反馈广义H₂控制

doi: 10.21656/1000-0887.420169

孙凤琪

吉林师范大学数学与计算机学院，吉林四平 136000

基金项目: 国家自然科学基金(61741318)

详细信息

作者简介:
孙凤琪（1968—），女，教授，博士（E-mail：1092748497@qq.com）

中图分类号: O231.2
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- 被引次数: 0
出版历程
- 收稿日期: 2021-06-22
- 录用日期: 2021-09-06
- 修回日期: 2021-09-06
- 网络出版日期: 2022-06-20
- 刊出日期: 2022-08-01

State Feedback Generalized H₂Control of Continuous Integrated Control Systems

SUN Fengqi

College of Mathematics and Computer, Jilin Normal University, Siping, Jilin 136000, P.R.China

摘要

摘要:
基于Lyapunov稳定性理论、矩阵分析法、线性矩阵不等式等方法，对同时带有控制输入和干扰输入的奇异摄动时变时滞不确定控制系统进行广义H₂控制研究。设计一个记忆状态广义H₂控制器，给出具体设计方法的判定定理。并对时滞依赖和时滞独立两种情形下采用新的引理，推出保守性相对更小的稳定性判据。对所得结论进行线性化处理，用数值样例验证了该文所得结论的有效性和可行性。指出在零到奇异摄动上界的整个区间范围内，闭环系统渐近稳定，扩大了广义H₂稳定空间，缩小了L₂-L_∞的性能指标。通过与相关文献进行稳定态指标对比，展示出该文所得方法具有一定的优越性和较小的保守性，并且适用于标准和非标准情形。
- Lyapunov稳定性 /
- 广义H₂控制 /
- 状态反馈控制器 /
- L₂-L_∞性能指标 /
- 交叉项界定法
Abstract:
Based on the Lyapunov stability theory, the matrix analysis method and the linear matrix inequality method, etc, the generalized H₂ control of singularly perturbed uncertain-control time-varying delay systems with control input and disturbance input, was studied. A memory state generalized H₂ controller was designed, and the decision theorem for the specific design method was given. With a new lemma for delay-dependent and delay-independent cases, the relatively less conservative stability criterion was derived. The obtained results were linearized, the selected numerical examples were used to verify the effectiveness and feasibility of the derived conclusions. The results show that, the closed-loop system is asymptotically stable in the whole range from zero to the singular perturbation upper bound, which expands the generalized H₂ stability space and reduces the L₂-L_∞ performance index. The comparison of the stability state parameter index with the related literatures indicate that, the proposed method has certain advantages and less conservatism, and is suitable for standard and non-standard cases.
- Lyapunov stability /
- generalized H₂ control /
- state feedback controller /
- L₂-L_∞ performance index /
- cross term definition method

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表 1 广义H₂稳定性能指标对比

Table 1. Comparison of generalized H₂ stability performance indicators

method	generalized H₂ control gain matrix ${\boldsymbol{K}}$	optimal ${L_2} {\text{-}} {L_\infty }$ performance index ${\gamma ^ * }$	perturbation upper bound $\bar \varepsilon $
ref. [12]	${ {\boldsymbol{K} }_1} = [ { - 22.046\;7}\quad{ - 14.167\;5} ]$	1.3255	0.3
ref. [12]	${ {\boldsymbol{K} }_2} = [ { - 22.037\;6}\quad{ - 12.656\;2} ]$	1.3255	0.3
theorem 2	${\boldsymbol{K}} = [ { - 2.252\;4}\quad{0.023\;6} ]$	1.1265	0.35
theorem 2	${{\boldsymbol{K}}_1} = [ {0.305\;7}\quad{0.044\;3} ]$	1.1265	0.35

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