Co-Design of Cryptographic Parameters and Delay-Aware Feedback Gain for Encrypted Control Systems

Encrypted control employs homomorphic encryption (HE) to protect both the computation and communication stages, making it a promising approach for secure networked control systems. Most existing results pre-design a controller in the plaintext domain and then implement it over encrypted data. However, this can be problematic because HE induces non-negligible communication and computation delays, which typically increase with the security level, potentially degrading control performance and even destabilizing the closed-loop system. To address this issue, we propose a co-design framework for cryptographic parameters and delay-aware feedback gain. We characterize the encryption-induced delay as a function of the cryptographic parameters and derive a sufficient condition for the existence of a stabilizing delay-aware feedback gain, expressed as a finite set of linear matrix inequalities. This leads to a tractable outer-inner design procedure that searches over cryptographic parameters that satisfy a desired security level and, for each such parameter, seeks a stabilizing feedback gain.