AUTHOR=Sato Masayuki , Sebe Noboru 

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

JOURNAL=Frontiers in Control Engineering

VOLUME=3

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=<p>This paper considers the conversion problem from unstructured linear time-invariant (LTI) controllers to <italic>observer-structured LTI controllers</italic>, 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, <italic>observer-structured LTI controllers</italic> 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 <italic>observer-structured LTI controller</italic> are parameterized with those of the given unstructured LTI controller, 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 the plant state and the <italic>observer-structured controller</italic> state for a stochastically defined non-zero initial plant state. Several toy examples are included to illustrate the effectiveness and the usefulness of <italic>observer-structured LTI controllers</italic>, and the utility of the proposed conversion parametrization.</p>