Observer design for loop transfer recovery and for uncertain dynamical systems

A theory of observer design for exact and approximate loop-transfer recovery (LTR) and for uncertain dynamical systems is given. The method decomposes a given multivariable nominal system into several single-input, single-output subsystems, each of which can be designed separately. Both full-order and reduced-order observer designs can be derived. The design addresses the case when uncertainties are modeled as blocks exterior to the given plant and the case when uncertainties are prescribed structurally in terms of a state-space description. When the uncertainties in a given plant are modeled external to it, the observer design corresponds to a traditional LTR design, When uncertainties are given in terms of a state-space description, observer design can take into account uncertain elements of both linear and nonlinear type. This analysis can be viewed as a contribution to the development of a separation principle under which control system design for an uncertain dynamic system can be decomposed into designing a state feedback law and an observer for implementing the state feedback design