State Feedback Control

Abstract

If a system is controllable all eigenvalues can be placed at arbitrary locations by static state feedback. Therefore, state feedback control can be used to stabilize the closed-loop system and to achieve further design specifications. Hence, the parameterization of state feedback controllers is an important aspect of control theory. In a system of the order n with one input u (i.e., a single-input system), the desired eigenvalues of the closed-loop system specify all n elements of the 1 × n state feedback gain k^T. If the system has p > 1 inputs (i.e., in a multiple input system), the desired eigenvalues again specify n elements of the p × n state feedback gain K. Therefore, after the assignment of the eigenvalues there remain (p − 1)n degrees of freedom parameterizing various properties of the closed-loop system as, e.g., the zeros in the elements of its transfer matrix.