Minimizing Unobservability for Linear Systems with Unmeasurable Periodic Disturbances

摘要

Linear systems excited by unmeasurable disturbances are very common in control systems. The state reconstruction of these systems via an augmented state vector leads in general to unobservability problems which must be overcome in order to build an observer. A geometric approach which avoids the computation of the observability matrix and gives a straightforward characterization of the unobservable subspace and an easy formulation for a canonical form for observability is developed. Then, assuming the a priori distribution of the disturbances to be known, an optimal canonical form for observability is derived in the sense that it minimizes the difference between the actual and estimate vector of the system.