OBSERVER DESIGN FOR LOOP TRANSFER RECOVERY AND FOR UNCERTAIN DYNAMIC-SYSTEMS

A new theory of observer design, for exact as well as approximate loop-transfer recovery (LTR) and for uncertain dynamical systems, is given. The method developed decomposes a given multivari-aUe 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 accomplished within the same framework. The developed 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. When the uncertainties in a given plant are modeled external to it, our observer design corresponds to a traditional LTR design. However, our design method is in the framework of “asymptotic Timescale and eigenstructure assignment.” Thus, it does not suffer from the inherent drawbacks of “repetitive design” and “stiffness” of design equations common to the existing methods of Kalman filter formalism and direct eigenstructure assignment. Furthermore, one can assign arbitrarily any chosen Timescale structure to the fast eigenvalues of the observer. In the case when uncertainties are given in terms of a state-space description, our observer design can take into account uncertain elements of both linear and nonlinear type. Any state feedback control law either linear or nonlinear which could stabilize the given uncertain system can be implemented via our observer without destroying the stability of the closed-loop system. In this sense, this work can be viewed as a theory of a separation principle for uncertain dynamical systems. © 1990 IEEE