# Compositional Synthesis of Symbolic Models for Networks of Switched Systems

## TL;DR

This paper introduces a compositional approach to create symbolic models for networks of discrete-time switched systems, enabling better analysis and control synthesis through dissipativity and passivity conditions.

## Contribution

It develops a novel compositional methodology using augmented-storage functions and alternating simulation functions for symbolic modeling of switched systems.

## Key findings

- Established a relation between switched subsystems and symbolic models using augmented-storage functions.
- Provided conditions under which symbolic models accurately approximate switched system behaviors.
- Validated the approach with two illustrative examples.

## Abstract

In this paper, we provide a compositional methodology for constructing symbolic models for networks of discrete-time switched systems. We first define a notion of so-called augmented-storage functions to relate switched subsystems and their symbolic models. Then we show that if some dissipativity type conditions are satisfied, one can establish a notion of so-called alternating simulation function as a relation between a network of symbolic models and that of switched subsystems. The alternating simulation function provides an upper bound for the mismatch between the output behavior of the interconnection of switched subsystems and that of their symbolic models. Moreover, we provide an approach to construct symbolic models for discrete-time switched subsystems under some assumptions ensuring incremental passivity of each mode of switched subsystems. Finally, we illustrate the effectiveness of our results through two examples.