Observability of systems with delay convoluted observation

Abstract

This paper analyzes finite dimensional linear time-invariant systems with observation of a delay, where that delay satisfies a particular implicit relation with the state variables, rendering the entire problem nonlinear. The objective is to retrieve the state variables from the measured delay. The first contribution involves the direct inversion of the delay, the second is the design of a finite dimensional state observer, and the third involves the derivation of certain properties of the delay - state relation. Realistic examples treat vehicles with ultrasonic position sensors.