LTR properties for output-delayed systems

출력 시간 지연 시스템의 루우프 복구특성

This paper presents robustness properties of the Kalman Filter ad the associated LQG/LTR method for linear time-invariant systems having delays in both the state and output. A circle condition relating to the return difference matrix associated with the Kalman filter is derived. Using this circle condition, it is shown that the Kalman filter guarantees(1/2, .inf.) gain margin and .+-.60.deg. phase margin, which are the same as those for nondelay systems. However, it is shown that, even for minimum phase plants, the LQG/LTR method can not recover the target loop transfer function. Instead, an upper bound on the recovery error is obtained using an upper bound of the solution of the Kalman filter Riccati equations. Finally, some dual properties between output-delated system and input-delayed systems are exploited.