# Stability and Robust Regulation of Passive Linear Systems

## TL;DR

This paper analyzes the stability of passive linear systems under interconnections, providing new conditions for various stability types and designing controllers for robust output tracking and disturbance rejection.

## Contribution

It introduces novel stability conditions for coupled passive systems and applies these to design controllers for PDEs with non-smooth signals.

## Key findings

- Established conditions for strong, exponential, and non-uniform stability.
- Designed passive error feedback controllers for robust output tracking.
- Demonstrated stability analysis with wave and heat equation examples.

## Abstract

We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the stability results to the construction of passive error feedback controllers for robust output tracking and disturbance rejection for strongly stabilizable passive systems. In the case of nonsmooth reference and disturbance signals we present conditions for non-uniform rational and logarithmic rates of convergence of the output. The results are illustrated with examples on designing controllers for linear wave and heat equations, and on studying the stability of a system of coupled partial differential equations.