H2 control and filtering of discrete-time LPV systems exploring statistical information of the time-varying parameters

This paper introduces a new strategy to improve performance in gain-scheduled control and filtering for LPV systems exploiting statistical information about the time-varying parameters whenever available. The novelty of the technique, named sub-domain optimization heuristic (SDOH), is to design controllers or filters treating robust stability independently of performance. The performance is optimized only in a sub-domain of the time-varying parameters, where a higher frequency of occurrence is expected, while the robust stability is certificated for the whole domain. The problem of gain-scheduled design subject to inexact measurements is discussed in details as main motivation but any other feedback or filter strategy for LPV systems were statistical information about the time-varying parameters is known can be handled in a similar way. Still in the context of inexact measurements, a more complete modeling for the additive uncertainty is given, generalizing previous results from the literature for two types of uncertainties, polytopic and affine. A new design condition for H2 full-order LPV filtering is also given as contribution. Several numerical examples are presented to illustrate the results.