Generalized PI observer design for linear systems

A parametric design approach for generalized proportional - integral (PI) observers of linear systems is proposed. Based on an explicit parametric general solution to a type of Sylvester matrix equations, complete parameterizations for all observer gains are presented. Moreover, the parametric expression of the left eigenvector matrix of the observer system is also established. The proposed design method can offer all the degrees of design freedom which can be utilized to achieve various desirable system specifications and performances. Also, a numerical example is given to show the design procedure and illustrate the effect of the proposed approach.