中文摘要：

针对同时具有干扰和时变输入时滞的挠性航天器的H∞控制问题,首先采用状态空间法描述一类具有干扰和输入时滞的挠性航天器模型;然后基于李亚普诺夫稳定理论和线性矩阵不等式（linear matrix inequality,LMI）法,通过构造一个新型的增广李亚普诺夫泛函,建立基于LMI形式的时滞相关的H∞状态反馈控制器设计方法,此法设计的反馈控制器增益依赖松弛矩阵而非正定的李亚普诺夫矩阵;最后,通过数值仿真验证该控制方法的有效性并分析其时滞量、H∞性能指标及时滞积分不等式分解系数对闭环系统性能的影响.与传统的设计相比,由于引入了松弛矩阵并在泛函求解过程中引入了时滞积分不等式分解系数,因此该设计方法既能提升设计的灵活性又能降低设计的保守性.

英文摘要：

In this paper, we address the H∞ control problem of flexible spacecraft experiencing disturbance and timevarying input delay. First, we adopt the state-space method to develop a flexible spacecraft model with disturbance and time-varying input delay. Next, based on the Lyapunov stability theory and using the linear matrix ineuality （LMI） method, we obtain an LMI delay-dependent H∞ state feedback controller by constructing a new augmented Lyapunov function. The designed feedback controller gain depends on slack variable matrices rather than on the non-positive definite Lyapunov matrix. Finally, we use numerical simulations to verify the effective- ness of the proposed method and to analyze the delays, the H~ performance index, and the influence of delay- integral-inequality decomposition coefficients on the closed-loop system performance. Compared with traditional methods, the proposed method improves the flexibility of the controller design and reduces design conservatism by introducing slack variables matrices and the delay-integral-inequality decomposition coefficient.