  We first propose systematic and comprehensive interval observer designs for
linear time-invariant systems, under standard assumptions involving
observability and interval bounds on the initial condition and disturbances.
Historically, such designs rely on transformations with certain limitations
into a form that is Metzler (for continuous time) or non-negative (for discrete
time). We show that they can be effectively replaced with a linear
time-invariant transformation that can be easily computed offline. Then, we
propose the extension to the time-varying setting, where conventional
transformations lack guaranteed outcomes. Academic examples are presented to
illustrate our methods.
