Complete Eigenstructure Assignment in High-order Descriptor Linear Systems via Proportional plus Derivative State Feedback

A parametric approach for eigenstructure assignment in the controllable high-order descriptor linear system A_mx^(m) + ... + A₁xdot + A₀x = Bu via proportional plus derivative state feedback control u = F₀x + F₁xdot + ... + F_mx^(m) is proposed. General parametric expressions in the direct closed forms for the closed-loop eigenvectors are presented, which are linear in a group of parameter vectors {f_i} which represent the degree of the design freedom. It is shown that the derivative feedback gain F_m may be taken to be an arbitrary real matrix satisfying a simple constraint, and the general expression for the proportional and derivative feedback F_i i = 0, 1, ..., m - l, are composed of both the group of vectors {f_i} and the derivative feedback gain F_m. The proposed approach does not impose any condition on the closed-loop finite eigenvalues, and assigns arbitrarily nm finite closed-loop eigenvalues. An example shows the effect of the proposed approach