Closed-loop transfer recovery with observer-based controllers. I - Analysis. II - Design

A detailed study is presented of three fundamental issues related to the problem of closed-loop transfer (CLT) recovery. The first issues concerns what can and cannot be achieved for a given system and for an arbitrary target CLT function (TCLTF). The second issue involves developing necessary and/or sufficient conditions for a TCLTF to be recoverable either exactly or approximately. The third issue involves the necessary and/or sufficient conditions on a given system such that it has at least one recoverable TCLTF. The results of the analysis identify some fundamental limitations of the given system as a consequence of its structural properties which enables designers to appreciate at the outset different design limitations incurred in the synthesis of output-feedback controllers. Then, the actual design of full-order or reduced-order observer-based controllers is addressed which will achieve as close as possibly the desired TCLTF. Three design methods are considered: (1) the ATEA method, (2) a method that minimizes the H2-norm of a recovery matrix, and (3) a method that minimizes the respective H(infinity) norm. The relative merits of the methods are discussed.