Characterization of discrete-time H2 control performance limitation based on poles and zeros

In this paper, we show that the best achievable performance in the H₂ regulation/tracking problem for discrete-time SISO systems can be expressed in a remarkably simple form by the poles/zeros of the plants and the poles of the closed-loop systems. We also explain that the poles of the closed-loop systems can be related with system parameters by an algebraic approach. Furthermore, corresponding expressions in the ¿-domain are given to reveal the relationship between the results in the z-domain and the s-domain. The derived expressions directly connect the system parameters and the resultant optimal H₂ performance and, therefore, they are effectively utilized in system parameter tuning.