# Exact recursive updating of uncertainty sets for discrete-time plants with a lag

## TL;DR

This paper introduces an exact recursive algorithm for updating the uncertainty sets of linear discrete-time systems with a lag, improving state estimation accuracy under bounded disturbances and noise.

## Contribution

It presents a novel recursive method specifically for plants with a lag, enhancing the existing set-based state estimation techniques.

## Key findings

- Efficient recursive updating of uncertainty sets for lag plants.
- Improved accuracy in state estimation under bounded disturbances.
- Applicable to systems with measurement noise and disturbances.

## Abstract

In a recent paper [arXiv:1612.04918] there are new results concerning the polytopic set of possible states of a linear discrete-time SISO system subject to bounded disturbances from measurements corrupted by bounded noise. Using these results we construct an algorithm which, for the special case of a plant with a lag, recursively updates these polytopic sets when new measurements arrive.