ℋ_∞ filtering for linear continuous-time systems subject to sensor non-linearities

In this study, the ℋ_∞ filtering problem for linear continuous-time systems subject to sensor non-linearities is considered. First, the global ℋ_∞ filtering is addressed by modelling the sensor non-linearities as sector non-linearities. The existence condition for an ℋ_∞ filter is derived for such systems by using both the circle criterion theory and Popov criterion theory. In both cases, design methods for ℋ_∞ filtering are proposed by means of linear matrix inequalities (LMIs)-based optimisation approach, which enables solutions to be found via efficient interior-point algorithms. To reduce the conservatism in the design of global ℋ_∞ filters for linear systems with output saturation non-linearities, the local ℋ_∞ filtering problem is considered. Local ℋ_∞ filtering refers that the states are within some bounded set while a regional L₂ gain is guaranteed. An LMI-based approach is developed to calculate parameter matrices of the local ℋ_∞ filter. Numerical examples are given to demonstrate the usefulness of the proposed results.