AUTHOR=Sato Masayuki , Sebe Noboru 

TITLE=Conversion From Unstructured LTI Controllers to Observer-Structured Ones for LPV Systems

JOURNAL=Frontiers in Control Engineering

VOLUME=Volume 3 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/control-engineering/articles/10.3389/fcteg.2022.804549

DOI=10.3389/fcteg.2022.804549

ISSN=2673-6268

ABSTRACT=This paper considers the conversion problem from unstructured Linear Time-Invariant (LTI) controllers to observer-structured LTI controllers, whose structure is similar to but not exactly the same as the so-called ``Luenberger observer-based controllers'', for Linear Parameter-Varying (LPV) plant systems. In contrast to Luenberger observer-based controllers, observer-structured LTI controllers can be defined and constructed even if the plant systems are given as LPV systems. In the conversion problem, the state-space matrices of the observer-structured LTI controllers are parametrized with those of the given unstructured LTI controllers, one free matrix, and a state transformation matrix. We also show a method to obtain the optimal state transformation matrix with respect to the convergence of the discrepancy between plant state and observer-structured controller state for non-zero initial plant state. Several toy examples are included to illustrate the effectiveness and the usefulness of observer-structured LTI controllers and the proposed conversion parametrization.