Modal optimal control procedure for near defective systems

This study discusses a modal optimal control procedure for defective system s with repeated eigenvalues. From the view point of mathematics, although n ear defective close eigenvalues are distinct, the characteristic of the sys tem is also defective. Therefore, we have to transform near defective syste ms into the defective one, and then modal optimal control procedure for the defective systems can be extended to deal with the corresponding problems for near defective systems with close eigenvalues. Because of the defective characteristic of the system, we have to use an invariant sub-space recurs ive method with numerical stability to calculate the generalized modes of t he defective and near defective systems. The Potter's approach is extended to solve the Riccati equations in the generalized model subspace of the def ective system. Because the order of the Jordan block matrix of the defectiv e eigenvalues, m, is much smaller than that of the state matrix, n, i.e., m much less thann, the present modal optimal control procedure is very simpl e and reduces the computing effort for the complex system with large number of degrees of freedom. A numerical example is given to illustrate and veri fy the validity of the procedure. (C) 2001 Academic Press.