Interval Observer Designs for Uncertain Linear Systems with State Lifting

This paper introduces an interval observer design with state lifting for discrete-time (DT) and continuous-time (CT) linear systems under additive bounded uncertainties. Our approaches circumvent the need for time-varying or time-invariant coordinate transformations by introducing two state lifting methods based on the Cayley-Hamilton theorem and a matrix exponential property. Further, it is demonstrated that the interval observers for the lifted system are at least as good as interval observers for the original non-lifted system with minimal increase in computational complexity, while also being applicable (feasible) to a broader range of systems due to the flexibility of increased degrees of freedom in the lifted observer. Finally, we demonstrate and discuss the effectiveness of the proposed approach on a wide range of CT and DT examples, including as a viable replacement for coordinate transformations.