Observer Design for Loop Transfer Recovery and for Uncertain Dynamical Systems

A general theory of observer design to achieve LTR is given. The method developed decomposes a given multivariable system into several single input single output subsystems each of which can be designed separately. The design method is in the frame work of `asymptotic pole placement', or more completely, it is in the frame work of time-scale structure and eigenvalue assignment. Thus it does not suffer from the inherent drawbacks of "repetitive design" and "stiffness" of design equations common to the existing methods viz observer design via Kalman filter formalism and via eigenstructure assignment. Both full order and reduced order observer designs can be accomplished with in the same frame work. Also, asymptotic LTR design as well as exact LTR design, whenever it can be done, can be formulated with in the same frame work. The developed observer design addresses not only the case when uncertainties are modeled as blocks exterior to the given plant but also the case when uncertainties are prescribed structurally in terms of a state space description. The designed observer can recover the corresponding robustness properties of either a linear or a nonlinear state feedback law. In this sense, this work can be viewed as a theory of a separation principle for uncertain dynamical systems.