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.