Asymptotically Stable 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 open. We show that, in some cases, no linear time-invariant change of coordinates can help to determine an exponentially stable interval observer. Next, we solve the problem by constructing interval observers of a new type, which have as key feature the property of being time-varying. This new design is applied to the chaotic Chua's system.