# Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems

## TL;DR

This paper introduces a distributed method for designing controllers in cascade interconnected systems to ensure passivity, enabling local design without full system knowledge and allowing incremental addition of subsystems.

## Contribution

A novel sequential, distributed control synthesis approach for cascade systems that guarantees passivity and supports modular addition of subsystems without redesign.

## Key findings

- Successfully ensures passivity in large-scale cascade systems.
- Enables local controller design with limited subsystem information.
- Supports incremental system expansion without redesign.

## Abstract

We consider the problem of designing distributed controllers to ensure passivity of a large-scale interconnection of linear subsystems connected in a cascade topology. The control design process needs to be carried out at the subsystem-level with no direct knowledge of the dynamics of other subsystems in the interconnection. We present a distributed approach to solve this problem, where subsystem-level controllers are locally designed in a sequence starting at one end of the cascade using only the dynamics of the particular subsystem, coupling with the immediately preceding subsystem and limited information from the preceding subsystem in the cascade to ensure passivity of the interconnected system up to that point. We demonstrate that this design framework also allows for new subsystems to be compositionally added to the interconnection without requiring redesign of the pre-existing controllers.