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

Abstract

A parametric approach for eigenstructure assignment in the controllable high-order descriptor linear system Amx(m) + ... + A1xdot + A0x = Bu via proportional plus derivative state feedback control u = F0x + F1xdot + ... + Fmx(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 {fi} which represent the degree of the design freedom. It is shown that the derivative feedback gain Fm may be taken to be an arbitrary real matrix satisfying a simple constraint, and the general expression for the proportional and derivative feedback Fi i = 0, 1, ..., m - l, are composed of both the group of vectors {fi} and the derivative feedback gain Fm. 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