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We introduce contracts for linear dynamical systems with inputs and outputs.Contracts are used to express formal specifications on the dynamic behaviour ofsuch systems through two aspects: assumptions and guarantees. The assumptionsare a linear system that captures the available knowledge about the dynamicbehaviour of the environment in which the system is supposed to operate. Theguarantees are a linear system that captures the required dynamic behaviour ofthe system when interconnected with its environment. In addition to contracts,we also define and characterize notions of contract refinement and contractconjunction. Contract refinement allows one to determine if a contractexpresses a stricter specifications than another contract. On the other hand,contract conjunction allows one to combine multiple contracts into a singlecontract that fuses the specifications they express.

Behavioural contracts for linear dynamical systems: input assumptions and output guarantees