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