一类不确定大系统的鲁棒指数控制

The Robust Exponential Stabilization Problem for Linear Large-scale Systems with Uncertainties

研究了一类不确定大系统的鲁棒指数控制问题.利用大系统分解方法,把大系统分解成若干个子系统.应用通常的最优控制方法,对每个孤立子系统设计适当的控制器,相应代数Riccati方程维数也较低从而易于求解.再综合子系统的控制器得到大系统的控制器.闭环系统的鲁棒指数稳定性通过Lyapunov第二方法证明.还举例说明了方法的有效性.

The robust exponential control problem for a class of large-scale systems with uncertainties is studied. By making use of the partition technique, we decompose the large-scale system into subsystems. Applying the standard linear quadratic optimal control method to each isolated nominal subsystem, we design controllers for all isolated nominal subsystems in terms of some lower dimension algebraic Riccati equations. Then we obtain a controller for the large-scale system by using controllers of isolated nominal subsystems. The robust stability of the closed loop system is proved by using Lyapunov′s second method.An example is included to show the solution methods.