Enhancement of security against zero dynamics attack via generalized hold

Zero dynamics attack is lethal to cyber-physical systems in the sense that it is stealthy and there is no way to detect it. Fortunately, if the given continuous-time physical system is of minimum phase, the effect of the attack is negligible even if it is not detected. However, the situation becomes unfavorable again if one uses digital control by sampling the sensor measurement and using the zero-order-hold for actuation because of the `sampling zeros.' When the continuous-time system has relative degree greater than two and the sampling period is small, the sampled-data system must have unstable zeros (even if the continuous-time system is of minimum phase), so that the cyber-physical system becomes vulnerable to `sampling zero dynamics attack.' In this paper, we begin with its demonstration by a few examples. Then, we present an idea to protect the system by allocating those discrete-time zeros into stable ones. This idea is realized by employing the so-called `generalized hold' which replaces the zero-order-hold.