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Closed-form solution to the non-homogeneous generalised sylvester matrix equation

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3 Author(s)
Wu, A.-G. ; Inf. & Control Res. Center, Harbin Inst. of Technol., Shenzhen, China ; Sun, Y. ; Feng, G.

A closed-form solution to the non-homogeneous generalised Sylvester matrix equation AV + BW = EVF + R, with the matrix F being in an arbitrary form, is proposed. The solution is expressed in terms of R-controllability matrices and observability matrices, and can provide all the degrees of freedom represented by a free parameter matrix. The proposed approach allows the matrices F and R to be set undetermined, and this feature may give great convenience and advantages in many applications of control systems design. A numerical example is given to illustrate the effect of the proposed approach.

Published in:

Control Theory & Applications, IET  (Volume:4 ,  Issue: 10 )