# On Instability of LS-based Self-tuning Systems with Bounded Disturbances

## TL;DR

This paper demonstrates that least-squares based self-tuning regulators for discrete-time linear systems can become unstable under any bounded disturbance, highlighting a fundamental limitation of these controllers.

## Contribution

It reveals the inherent instability risk of LS-based self-tuning regulators in the presence of bounded disturbances, even if the noise is minimal.

## Key findings

- LS-based STR can destabilize systems with bounded disturbances
- Instability risk exists regardless of disturbance magnitude
- Highlights limitations of LS-based self-tuning control methods

## Abstract

It is well known that discrete-time linear systems can be stabilized by a least-squares (LS) based self-tuning regulator (STR), as long as noises are absent. However, this note shows that once the discrete-time linear systems are disturbed, the LS-based STR is always running the risk of unstabilizing systems, no matter how small the noises are.