# Robust Hybrid Output Regulation for Linear Systems with Periodic Jumps: the non-semiclassical case

## TL;DR

This paper presents a robust hybrid output regulation method for uncertain linear systems with periodic jumps, introducing a novel regulator design that includes data-driven estimation and internal models for flows and jumps.

## Contribution

It develops a non-semiclassical approach to robust output regulation for hybrid MIMO systems with uncertainties and periodic jumps, overcoming previous restrictive assumptions.

## Key findings

- Proposes a three-unit regulator design combining data-driven estimation and internal models.
- Provides necessary conditions for robust regulation in hybrid systems with uncertainties.
- Achieves regulation without restrictive assumptions used in prior works.

## Abstract

This paper solves the robust hybrid output regulation problem for arbitrary uncertain hybrid MIMO linear systems with periodic jumps without the restrictive assumptions used in all previous works on the subject. A necessary condition for solving the problem is that the regulator must incorporate an internal model of the flow zero-dynamics, which is typically affected by uncertainties and then unknown. Hence, the proposed regulator consists of three units: a data-driven estimator of the dynamics that are invisible from the regulated output during flows, a flow internal model in charge of achieving regulation during flows, and a jump internal model in charge of imposing a suitable reset of the state at each jump.