Design of observers for descriptor systems using a descriptor standard form

Methods are developed for constructing Luenberger-type observers for linear time-invariant descriptor systems. Based on the descriptor standard form derived here by means of a simple matrix calculus, full-order observers, reduced-order observers and function observers of a general type are proposed. Some necessary and sufficient conditions for the function observers to estimate linear functions of the state are discussed. Then, the so-called separation property of combined observer-controller systems is established.