定常线性系统的正性和最优性

POSITIVITY AND OPTIMALITY FOR LINEAR MULTIVARIABLE TIME-INVARIANT SYSTEMS

中文摘要

      本文从正实函数和最优控制系统理论出发，讨论了定常线性系统的正性和最优性之间的关系，从而得出，一个定常线性系统经稳定的常增益最优状态反馈后得到的闭环系统是正的；反之，一个正系统，经过单位输出负反馈得到的闭环系统是稳定的和最优的。

英文摘要

      In this paper, the relationships of positivity and optimality for linear time-invariant systems are considered. First, the relationship of positivity and optimality for single-input single -output linear time -invariant systems is discussed by the frequency domain method. Next, for multivariable linear time -invariant systems, this relationship is discussed by the time domain method. The main results are as follows: The closed loop system formed by stable optimal state feedback is positive. Its transfer function matrix is positive real. Conversely, if the open loop transfer function matrix is positive real, then the closed loop system obtained by negative unity output feedback is stable and optimal. Finally, from the discussion of the relationships of positivity and optimality we showed that the stable gain margin OGTT optimal control systems is infinite.