H-INFINITY CONTROL AND ESTIMATION PROBLEMS WITH DELAYED MEASUREMENTS - STATE-SPACE SOLUTIONS

Most physical processes exhibit transport delay in the measured output , and it is well known that this can have disastrous effects on system stability and performance if it is not accounted for. In this paper, we give necessary and sufficient conditions for existence of estimator s and controllers that achieve the desired H-infinity, performance cri terion when such a measurement delay is present. We also give the comp lete characterization of all controllers and estimators that achieve t he desired performance criterion. The necessary and sufficient conditi ons are easy to check and are given in terms of the familiar pair of a lgebraic Riccati equations that appear in the nondelay versions of the corresponding H-infinity problems, along with an additional Riccati d ifferential equation. Explicit state-space formulas for the controller s and estimators are also obtained. They have a linear periodic struct ure and are easily implementable. To obtain these results, we first ob tain state-space results for a ''modified'' Nehari problem, which may be of independent interest (see Problem 5 in section 2).