Functional observer design with application to pre-compensated multi-variable systems

Partial state estimation of dynamical systems provides significant advantages in practical applications. Likewise, pre-compensator design for multi variable systems invokes considerable increase in the order of the original system. Hence, applying functional observer to pre-compensated systems can result in lower computational costs and more practicability in some applications such as fault diagnosis and output feedback control of these systems. In this note, functional observer design is investigated for pre-compensated systems. A lower order pre-compensator is designed based on a H2 norm optimization that is designed as the solution of a set of linear matrix inequalities (LMIs). Next, a minimum order functional observer is designed for the pre-compensated system. An LTI model of an irreversible chemical reactor is used to demonstrate our design algorithm, and to highlight the benefits of the proposed schemes.