Design of causal state observers for regular descriptor systems

In this contribution a new framework for the design of causal state observers for regular descriptor systems is developed. The proposed procedure is derived on the basis of well-known and slightly modified parametric design concepts for state feedback controllers and generalized state observers. The resulting method can be applied under some necessary and sufficient, and thus minimal, existence conditions for causal state observers. The relation between the generalized observer and the observer in state space form is given by a suitable coordinate transformation. In general, neither controllability nor observability or any specific system representation is required. The separation principle holds.The proposed procedure is applied to two examples, namely a differentiating system which can be observed by a causal state observer and a double-beam vibration control problem.