Solvability and complete parametric approach for output regulation problems of matrix second-order systems via error feedback

We consider the output regulation problem for matrix second-order systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated directly in the matrix second frame work. It is given that the solvability of output regulation problem equals to the solvability of regulation equations MIIS²+DIIS+KII=BΓ+P and RIIS+CII+Q=0. Moreover, complete parametric expressions for feedback gain matrices are established by the method of solving linear equations. A numerical example demonstrates the effect of the proposed method.