Contract theory based on differential-algebraic equations

In the field of systems engineering, contract-based design [1] is a modular methodology that enables independent component development while ensuring correct system-wide integration. This contract-based perspective supports modular and compositional system design:

(i) Each subsystem can be designed independently under its own contract.

(ii) When composing systems, one can verify compatibility between contracts by checking that assumptions and guarantees are consistent.

(iii) Contracts provide a formal interface for verifying correctness, safety, and performance across components.

The goal of this project is to extend contract theory to differential–algebraic equations (DAEs). Mathematically, DAEs offer several potential advantages for contract-based analysis:

(1) System interconnections can be naturally expressed as algebraic equations, supporting a compositional framework.

(2) DAEs treat all variables uniformly—states, inputs, and outputs—aligning well with the behavioral approach.

(3) The geometric analysis of DAEs is well established, providing effective tools for describing relations between systems and specifications.

[1] A. Benveniste, B. Caillaud, et all, Contracts for System Design. Foundations and Trends in Electronic Design Automation, Now Publishers, 2018.