中文摘要：

针对大型土木工程结构,研究了具有完整性的小增益分散稳定化容错控制问题,考虑子控制系统关联项及系统中传感器与作动器出现故障的情况,利用Lyapunov稳定性理论及线性矩阵不等式方法,给出了离散时滞关联系统分散镇定的充分条件,并证明了该条件等价于一组线性矩阵不等式的可行性问题。进而,通过建立和求解一个凸优化问题,提出了具有完整性的小反馈增益参数分散稳定化容错状态反馈控制律的设计方法,所得到的子系统控制器能保持全局渐进稳定。针对ASCE 9层benchmark模型,该文分别从部分独立分散控制和重叠分散控制角度研究分析了正常工况、传感器失效、作动器失效及传感器作动器均失效工况的分散控制设计与数值分析。结果表明,该文提出的小增益分散稳定化控制（LMI-SGDSC）算法能获得与集中控制策略接近的控制效果,且无需更多的控制能量;相对于集中控制,重叠分散控制系统具有更高的可靠性;在发生故障时,具有完整性的分散稳定化容错控制（LMI-SGFTDSC）具有较好的控制效果。

英文摘要：

The issue of fault-tolerant decentralized control is investigated for large-scale civil engineering structures. Considering the correlation of the sub-control system, the sensor failures and the actuator failures, a sufficient condition for decentralized stabilizability is proposed for the class system of discrete-time systems with delay interconnections by using the Lyapunov stability theory and the linear matrix inequality （LMI） approach. It is shown that this condition is equivalent to the feasibility problem of the linear matrix inequality. Furthermore, a decentralized state feedback control law is derived as a convex optimization problem, and the latter can be solved by using existing efficient convex optimization techniques. The obtained controller enables the closed-loop systems to be stable. Considering sensor failures and the actuator failures, the ASCE 9-story benchmark building is selected as a numerical example to evaluate the control performance of the partially independent decentralized control and overlapping decentralized control. Numerical simulation results indicate that the proposed small gain decentralized stabilization control （LMI-SGDSC） algorithm performs as well as the traditional centralized control, and the overlapping decentralized control has a greater level of reliability. The fault tolerant decentralized control （LMI-SGFTDSC） achieves satisfactory control effects.