A simplified design of state-feedback controllers with prescribed damping

In linear time invariant (LTI) system design, the implementation of stabilizing state feedback based on eigenvalue assignment has been established as a standard. In this frame, a new solution is proposed with a twofold purpose: i) to decisively relax the high calculation effort needed in traditional pole placement techniques, especially for high-order multi-input systems, and ii) to simultaneously assign all the closed-loop system eigenvalues to have a desired common real part on the left-half complex plane. This is particularly useful in many real-world applications where dominant damping is a prerequisite condition for advanced designs of complex high-order systems. The proposed approach is based on the idea of utilizing Lyapunov techniques not only as examining methodologies of the system stability, but also as designing tools. In this framework, by keeping the predefined damping constant as the only parameter, the method is very simple since it needs the construction of a typical Lyapunov equation, for which it is a priori known that a solution exists. The proposed approach is validated on two practical examples from the area of power systems, firstly in the case of a multi-level converter and secondly in a dc microgrid application with two dc/dc buck converters feeding local constant current loads and linked through a distribution line.