  Encrypted dynamic controllers that operate for an unlimited time have been a
challenging subject of research. The fundamental difficulty is the accumulation
of errors and scaling factors in the internal state during operation.
Bootstrapping, a technique commonly employed in fully homomorphic
cryptosystems, can be used to avoid overflows in the controller state but can
potentially introduce significant numerical errors. In this paper, we analyze
dynamic encrypted control with explicit consideration of bootstrapping. By
recognizing the bootstrapping errors occurring in the controller's state as an
uncertainty in the robust control framework, we can provide stability and
performance guarantees for the whole encrypted control system. Further, the
conservatism of the stability and performance test is reduced by using a lifted
version of the control system.
