$\mathscr{H}_{2}$ gain-scheduled filtering for discrete-time LPV systems using estimated time-varying parameters

This paper investigates the problem of gain-scheduled filtering for discrete-time LPV systems where the scheduling parameters cannot be measured, but only estimated. Differently from the existing methods that are suitable to deal with inexact measures, the design of the gain-scheduled filter is guided by some information provided by the estimation algorithm. As a consequence, the proposed procedure puts in evidence a trade-off that must be evaluated by the designer involving: guarantee of stability, performance and the required on-line computational effort. The overall result is a better evaluation of the true improvement that can be achieved by the gain-scheduled filters with respect to the robust filters (where the real-time availability of the scheduling parameters is not necessary). Some technical contributions to reduce the conservativeness of the synthesis conditions, given in terms of LMI relaxations, are also provided as well a case study to illustrate the approach.