General Structured Observers for Discrete-Time Linear Systems

A class of general structured discrete-time deterministic observers is developed. The one-step predicting or Luenberger observers and the current-update observers may be obtained from this class of general structured observers. Interesting relationships and important properties among various full-order observers are established. Optimal discrete-time observer gains are then derived, and it is shown that the optimal observers can be structually and numerically equivalent to various forms of Kalman filters.