Interval observers for planar systems with complex poles

In some parametric domains, the problem of designing an exponentially stable interval observer for an exponentially stable two dimensional time-invariant linear system is an open problem. We show that, in some cases, no linear time-invariant change of coordinates can help to construct exponentially stable interval observers. Next, we exhibit a time-varying change of coordinates transforming the original system into a form for which exponentially stable interval observers can be easily constructed. An interval observer is then presented in the case where additional disturbances are present in the dynamics, and applied to the chaotic Chua's system.