On zeros of sampled-data system with relative degree two

Unstable zeros limit the achievable control performance. When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold, at least one of the zeros of the resulting sampled-data model is unstable for small sampling periods. Thus, attention is here focused on continuous-time systems with relative degree equal to two. This paper analyzes the zeros of the sampled-data models corresponding to the continuous-time systems mentioned above and gives approximate expressions of the zeros in the form of a power series expansions up to the fourth order term of sampling period. Meanwhile, the stability of the zeros is discussed for small sampling periods and a new stability condition is derived. It is further extension of the previous result.