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Gain-Scheduling and Linear Parameter-Varying (LPV) Control are among
the most popular and effective strategies to handle time-varying
uncertainties and nonlinearities in feedback control systems. In this
talk we revisit various issues in the design of controllers and
estimators for LPV systems, in particular for systems in which
parameter variation is present at the input and output matrices of the
system’s state-space realization. We start with the bad news, by
showing that popular strategies for handling such type of parameter
variation that introduce pre- and post-filters are generally not
effective, followed by some good news. The good news include some new
lifts that allow the handling of such systems without resorting to
pre- and post-filtering and the proof that some existing conditions
for the design of estimators for LPV systems which were believed to be
only sufficient are indeed necessary as well.
