Reduced-order performance of parallel and series-parallel identifiers with weakly observable parasitics (Q790766)

A class of discrete systems \[ x(k+1)=A_{11}x(k)+\mu A_{12}z(k)+B_ 1u(k), \] \[ z(k+1)=A_{21}x(k)+\mu A_{22}z(k)+B_ 2u(k), \] \[ y(k)=C_ 1x(k)+\mu C_ 1x(k)+\mu C_ 2z(k)\in E^ 1, \] is considered where \(A^{-1}\!_{11}\) exists and \(\mu\) is a small positive parameter. The identifier for the system is a linear form of x(j), z(j), u(j), \(j=1,...,n\). When parasitics in the input equal zero, the identifier equals zero. The identifier is applied to the actual system with parasitics. The purposes of the paper are to examine the robustness of ''parallel'' and ''series-parallel'' identifiers in the presence of parasitic input, obtain bounds for their parameters and output errors, and thereby examine their performances.