LOOP TRANSFER RECOVERY FOR LINEAR-SYSTEMS WITH DELAYS IN THE STATE AND THE OUTPUT

This paper presents robustness properties of the Kalman filter and the associated LQG/LTR method for linear time-invariant systems having de lays in both the state and the output. A circle condition relating to the return difference matrix associated with the Kalman filter is deri ved. Using this circle condition, it is shown that the Kalman filter g uarantees (1/2, infinity) gain margin and +/-60 degrees phase margin, which are the same as those for non-delay systems. However, it is show n that, even for minimum phase plants, the LQG/LTR method cannot recov er the target loop transfer function. Instead, an upper bound on the r ecovery error is obtained by using an upper bound of the solution of t he Kalman filter Riccati equations. Finally, some dual properties betw een output-delayed systems and input-delayed systems are exploited.