This work deals with a novel theoretical framework,
based on the algebra of Volterra linear integral operators,
aimed at designing non-asymptotic state observers for
continuous-time SISO linear systems. We show that the design
of observers with finite-time convergence of the estimation error
can be carried out by appropriately choosing the kernels of
Volterra operators applied to the measured input and output
signals. The kernel-based state estimator can be implemented
as a finite-dimensional linear time-varying dynamical system,
that is BIBO stable with respect to the input and output
injections. The properties of the kernels guaranteeing nonasymptotic
convergence of the state estimate are analyzed and
simulations are given to compare the proposed methodology
with existing approaches.
