Non-asymptotically stable observers for linear time-invariant systems

The concept of asymptotical observation is extended to include a new kind of observers which converge asymptotically not to the (unknown) state of a given system as conventional observers do but rather to an arbitrarily small neighborhood of the state. This type of convergence represents a natural technical requirement in applications and leads to the broadest class of models for asymptotic state estimation. Non-asymptotically stable observers are shown to be robust and to possess closed-loop stability properties under permanently acting disturbances. They require a bit of additional pointwise information and detectability condition is no longer necessary. In linear time-invariant case such models are conditionally stable in the large in the sense specified below.