Observers for Interval Systems using Set and Trajectory-based Approaches

In this paper, set and trajectory-based approaches to interval observation of uncertain systems are presented and compared. The kind of uncertain systems considered are those systems described by a discrete linear time-invariant model with parameters bounded in intervals. The aim of this paper is to study the viability of using set-based approaches coming from the interval analysis community to solve the interval observation problem. Set-based approaches are appealing because of a lower computational complexity compared to trajectory-based approaches but they suffer from the wrapping effect and do not preserve uncertain parameter time-invariance. On the other hand, trajectory-based approaches are immune to these problems but their computational complexity is higher. However, these two families of approaches are equivalent when the observer satisfies the isotonicity condition, which give criteria to tune the observer gain. Finally, these two families of interval observation philosophies will be presented, analysed and compared by using them in an example.