Observer Design for Nonregular Descriptor Systems with Unknown Inputs in Finite Time

The problem of inputs decoupled observer design in finite time for nonregular descriptor systems with unknown inputs was considered. Based on the constructive characteristic of the descriptor systems and under some general assumptions, a new nonsingular transformation of the input-state pair of descriptor systems was introduced, which transforms the nonregular descriptor system with unknown inputs into one of standard state-space systems where the inputs were known by regarding the partial state as unknown inputs. The sufficient conditions for the existence of the observer and simple method to design the observer are given, and the state and unknown inputs of the descriptor systems are exactly estimated by the state of observer and output of descriptor systems in finite time