多模型系统最优同时镇定状态反馈控制器设计算法

对于一类可以用有限多个状态方程来描述其动态特性的多模型系统，研究了同时镇定最优状态反馈控制器设计问题，即设计一个状态反馈控制器，使得闭环系统渐近稳定，并对指定的二次型性能指标进行优化．文中在导出闭环系统渐近稳定的充分性条件的基础上，探讨给定二次型性能指标的优化问题，并最终将该状态反馈控制器的设计问题转化为基于线性矩阵不等式（ＬＭＩ）的凸优化问题进行求解．由于将原问题转化为凸优化问题，确保了求得的解必定为全局最优解．最后给出了两个实际系统的设计算例，其结果表明了算法的有效性．

Optimal Simultaneous Stabilization of Multi-Model Systems by State Feedback Controller

The problem of designing an optimal state feedback simultaneous stabilizer for multi model systems whose dynamics is described by finite state equalities was considered. In the control scheme, a state feedback controller was designed to make the closed loop system stable asymptotically and the given quadratic index optimal. Sufficient condition for the closed loop system to be asymptotically stable was given, based on which the problem of optimality was considered then. The problem of designing such a controller was finally converted to a convex optimization problem constrained by linear matrix inequalities. In such a way, the final solution is ensured to be global optimal. In the end, the effectiveness of the proposed algorithm was demonstrated by two design examples.