Secure and Private Control Using Homomorphic Encryption via Multi‐Lyapunov Functions

Traditional dynamic resetting output‐feedback controllers can address the so‐called overflow problem in the encrypted control domain. However, the synthesis of such resetting controllers based on a single Lyapunov function generally leads to overly conservative results. To overcome this limitation, this paper proposes an improved dynamic resetting output‐feedback controller that incorporates additional design parameters to achieve enhanced control performance. Moreover, two distinct Lyapunov functions are employed for different resetting phases, which significantly reduces conservatism in the encrypted control framework. Finally, a numerical example is provided to demonstrate the effectiveness and efficiency of the proposed approach.