Open‐Loop Functional Observer and State Feedback for Linear Systems Using Multirate Output Sampling

In this paper, the problem of estimating a linear functional of the state vector is considered in order to implement a feedback control law for discrete‐time linear multivariable systems. The proposed method is based on multirate sampling of the plant output. We give necessary and sufficient conditions for the existence of the functional observer, and propose a functional observer with the minimal number of output samples. In this work, the control law is implemented using the output samples, thus this methodology is more practical than state based techniques. A numerical example is considered to illustrate the procedure and highlight the advantages of the proposed method.