Book Description

The theory of observers for linear, time invariant systems is generalized to systems where some of the system inputs are unmeasurable (or inaccessible) and statistically unknown. Criteria for the existence of such observers for systems with a single output and a single unknown input are developed. When the number of unknown inputs is equal to the number of system outputs, it is shown that the observer may be decomposed into a set of equivalent single output, single unknown input systems for which the previous results apply. For systems with more outputs than unknown inputs, a minimal number of outputs, derived from linear combinations of the original system output is examined. For sampled data measurements, it is shown that there are considerable practical advantages to sampling an ovserver error signal rather than the system outputs and inputs directly. A solution for the initial system state corresponding to the continuous-time stochastic smoothing filter is obtained. (Author).