Linear Quadratic Regulation and Tracking using Output Feedback with Direct Feedthrough

Abstract

This paper presents the development of linear quadratic regulation and output tracking algorithms using output feedback when both the measurement and performance output equations contain direct feedthrough terms. Although all physical systems can be modeled without direct feedthrough, there are still many situations where system models with direct feedthrough are important. For this situation, we modify previous work on the same topic for systems without direct feedthrough. It is shown that for the regulation problem, the optimal output feedback gain for a direct feedthrough case can be directly obtained, via a transformation, from the approach used for systems without direct feedthrough. However, for the tracking problem, a new set of coupled matrix equations for determining the optimal output feedback gain is derived from the necessary conditions for minimizing the cost function. The effectiveness of the developed algorithms is demonstrated using numerical examples