Delta算子不确定系统的鲁棒H_2/H_∞控制

Robust H_2/H_∞ Control for Delta Operator Uncertain System

研究了Delta算子描述的同时具有模型范数有界参数不确定性和外部扰动的一类系统的鲁棒H2/H∞控制问题。运用线性矩阵不等式(LMI)方法,证明了鲁棒H2/H∞控制律存在的充分必要条件,然后用一个线性矩阵不等式的可行解给出所有这一控制律的一个参数化表示,进一步通过建立和求解一个凸优化问题,给出了最优鲁棒H2/H∞控制律的设计。最后,用一个例子验证了给出方法的可行性。

The problem of H2/H∞ robust control for delta operator formulated a kind of linear systems with norm--bounded model parameter uncertainty and exterior disturbance was considered. A sufficient and necessary conditions and the corresponding state feedback control law were derived in terms of linear matrix inequality. It is showed that this condition is equivalent to the feasible solutions problem of a linear matrix inequality and its solutions provide a parameterized representation of the controller. Furthermore, the design problem of optimal robust H2/H∞ controller was given by solving a corresponding convex optimization problem. Finally, an example was given to illustrate the feasibility of the presented method.