ℋ2 gain-scheduled design subject to inexact measurements: performance comparison of two models for additive uncertainty

This paper investigates the problem of ℋ2 gain-scheduled design (control and filtering) for LPV systems where the scheduling parameters are affected by additive noises. The purpose is to analyze the impact on the ℋ2 performance of two models commonly used to model the additive uncertainty, one considering that the bounds for the noise parameters are dependent of the values of the scheduling parameters (the saturation effect is taken into account) and the other not. In this sense, a control design example is presented to illustrate that if the saturation effect is considered, a finite and smaller upper bound to the ℋ2 norm is achieved and, on the other hand, if the saturation is neglected, the system may be not stabilized. A filter design example is also presented to show that both the ℋ2 guaranteed cost and the associated time-dependent performance indexes (MSE and SDMSE) are reduced when considering saturation.