Kernel-based non-asymptotic state estimation for linear continuous-time systems

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 non-asymptotic convergence of the state estimate are analyzed and simulations are given to compare the proposed methodology with existing approaches.