# Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

## TL;DR

This paper develops an interval predictor for linear parameter-varying systems with uncertainties, ensuring stability through Lyapunov functions and linear matrix inequalities, with applications in autonomous vehicle motion planning.

## Contribution

It introduces a novel Lyapunov-based interval predictor for uncertain systems with unmeasurable parameters, formulated via linear matrix inequalities.

## Key findings

- The predictor guarantees stability under specified conditions.
- Application to autonomous vehicles demonstrates practical effectiveness.
- The approach handles unmeasurable parameters and uncertain inputs.

## Abstract

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.