Rigorous constraint satisfaction for sampled linear systems

TL;DR

This paper introduces a numerical method to rigorously verify constraint satisfaction in sampled linear systems, combining global optimization techniques with interval matrix exponential bounds for improved accuracy.

Contribution

It presents a novel algorithm that ensures rigorous verification of constraints in sampled linear systems using advanced bounding techniques.

Findings

The method guarantees constraint satisfaction verification between sampling points.

It effectively combines branch and bound schemes with interval matrix exponential bounds.

The approach enhances the reliability of control in sampled linear systems.

Abstract

We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling instances. The proposed algorithm combines elements of classical branch and bound schemes from global optimization with a recently published procedure to bound the exponential of interval matrices.