非方离散广义系统的奇异LQ问题及最优代价单调性

Singular LQ problem and the optimal cost monotonicity of rectangular discrete-time descriptor systems

研究了非方离散广义系统的奇异线性二次指标最优控制问题(即LQ问题).在给定的条件下,给出LQ问题的惟一最优控制和最优状态,并将最优控制综合为状态反馈.闭环系统的所有有限特征值均在开单位圆内,闭环系统的状态有最少自由元.并给出非方离散广义系统的最优代价比较定理.

A singular linear quadratic （LQ） problem for rectangular discrete-time descriptor systems is investigated. Under some conditions, the unique optimal control and the unique optimal state of the LQ problem are given. The optimal control is synthesized via state feedback, All the finite eigenvalues of the closed-loop system are located in the open unit disc. The state of the closed-loop system has the least free entries. The comparison theorem of the optimal cost of rectangular diserete-time descriptor systems is given.