线性系统静态输出反馈保性能控制

摘要

Classes of fault-tolerant controller design methods based on linear matrix inequality are supplied, which can guarantee the optimal performance of system upon correct fault detection and also ensure the asymptotic stability of system even upon incorrect online detection while researching on the remote fault diagnosis of dyeing &finishing equipment. With projection theorem, the continuous static output feedback controller design problems can be transformed into a class of solvable linear matrix inequality (LMI) problems excluding equality constraint, and then the minimum performance index of closed-loop system can be obtained via solving a class of contained LMI constraint convex optimization problems. Finally, the validity of the algorithm is verified with numerical examples.%研究在对染整设备进行远程故障诊断时，给出一类基于线性矩阵不等式的主动容错控制器设计方法，能保证在正确故障检测的情况下，系统性能达到最优，同时在不正确的在线检测情况下，系统也能达到渐近稳定。利用投影定理，将连续系统的静态输出反馈控制器设计问题转化为一类不含等式约束的线性矩阵不等式(LMI)可解性问题，进而通过求解一类含有LMI约束的凸优化问题得到闭环系统的最小性能指标。最后通过数值例子验证算法的有效性。