Estimatable linear systems

A well-posed linear system is said to be optimizable if for any initial state, an input function in L² can be found such that the state trajectory is in L² (this is also known as the finite cost condition). The dual property, estimatability concerns the possibility of estimating the final state of the system at time t = 0, based on the knowledge of its output function for all negative time. We explore these properties, their duality, their optimal versions, and their connection with stabilizability and detectability.