LTR DESIGN OF DISCRETE-TIME PROPORTIONAL-INTEGRAL OBSERVERS

This paper applies the proportional-integral (PI) observer in connecti on with loop-transfer recovery (LTR) design for discrete-time systems. Both the prediction and the filtering versions of the PI observer are considered. We show that a PI observer makes it possible to obtain ti me recovery, i.e., exact recovery for t --> infinity: under mild condi tions. Two systematic LTR design methods, one based on an extension of the linear quadratic Gaussian loop-transfer recovery (LQG/LTR) and th e other based on linear matrix inequality (LMI), are derived for the d iscrete-time PI observer case. Explicit expressions for the recovery e rror when exact recovery is not achievable for all frequencies are als o given.