不确定离散时间系统的H_2/H_∞最优保性能控制

H_2/H_∞ Optimal Guaranteed Cost Control of Uncertain Discrete-time Systems

针对具有两个不同被调输出的一类不确定离散时间系统 ,研究其 H2 / H∞ 状态反馈保性能控制问题。基于线性矩阵不等式处理方法 ,推导出存在 H2 / H∞ 保性能控制律的充分必要条件 ,并用一个线性矩阵不等式的可行解给出了所有保性能控制律的参数化表示。进而通过建立和求解一个凸优化问题 ,给出了 H2 / H∞ 最优保性能控制律设计方法。

The H2/H∞ guaranteed cost control problem via state feedback controllers is considered for a class of uncertain discrete-time systems with two controlled outputs. Based on the linear matrix inequality (LMI) approach, a necessary and sufficient conditions are derived for the existence of guaranteed cost controllers, and a parameterized characterization of all guaranteed cost controllers, if exist, is provided in terms of the feasible solutions to a certain LMI. Furthermore, the design problem of the H2/H∞ optimal guaranteed cost controller is formulated as a convex optimization problem, which can be efficiently solved by existing convex optimization techniques. An example is given to illustrate the effectiveness of the proposed results.