Abstract
For a linear time-invariant discrete-time system such that the observability index is two, this paper proposes a new observer which estimates unmeasured states and unknown inputs simultaneously. Linear transformation plays an important role in design of the observer. It is performed to obtain an output error equation which is decoupled from the estimation errors of unmeasured state variables. Based on this error equation, the observer is designed by a state feedback control theory. Essentially, the unknown input is estimated without influence of the estimation error of the state. If the unknown input is constant, both the state and the input can be reconstructed exactly in finite time. Under a certain condition, the observer works as a minimal-time deadbeat state observer which is completely insensitive to any unknown input.
