Delta算子不确定系统的区域极点约束保性能控制

Guaranteed Cost Control with Pole Constrains for Delta Operator Uncertain Linear Systems

研究了Delta算子描述下的具有范数有界参数不确定线性系统的圆形区域极点配置的保性能控制问题。运用线性矩阵不等式(LMI),把Delta算子闭环极点配置在D区域内,证明了保性能控制律存在的充要条件,并通过建立和求解一个凸优化问题,给出了具有极点约束的保性能控制设计。仿真例子验证了方法的可行性。

The problem of guaranteed cost controller with circular pole constrains for delta-operator linear systems with norm-bounded parameter uncertainty is focused on. At first, the closed poles are located within a specific circular region and a necessary and sufficient condition for the existence of guaranteed cost controllers is derived in terms of linear matrix inequalities. It is shown that two conditions are equivalent to the solvability problem of the linear matrix inequalities, and its solutions provide a parameterized representation of guaranteed cost controller. Secondly, the designed problem of the guaranteed cost controller with circular pole constrains is given by solving a corresponding convex optimization problem. At last, an example is given to illustrate the effectiveness of the results.