Interval observers for linear systems with additive disturbances*

It is shown that, for any time-invariant exponentially stable linear system with additive disturbances, time-varying exponentially stable interval observers can be constructed. The technique of construction relies on the Jordan canonical form that any real matrix admits and on time-varying changes of coordinates for elementary Jordan blocks which lead to cooperative linear systems. The approach is applied to any non-linear system that can be written as the sum of a linear stable term, and of a non-linear term (including disturbances) for which known bounds exist.