Chained eigenstructure assignment for constant-ratio proportional and derivative (CRPD) control law in controllable singular systems

Abstract

This paper deals with chained eigenstructure assignment for controllable singular systems of the form E ̂ x ̇ (t) = A ̂ x(t) + B ̂ u(t) with constant-ratio proportional and derivative (CRPD) control of the form u(t) = μKx(t) − K x ̇ (t) + w(t) . The closed-loop system exhibits the following features: regularity, impulse-free response, and arbitrary eigenvalue (except open-loop poles) assignment. This parametric characterization conveniently chooses the nonunique gain matrix K to modify the dynamic response of the system. An illustrative example is included to demonstrate our approach.