Robust pole assignment using closed loop controllability conditions

The problem of optimal selection of closed loop eigenvalues for single input systems is discussed. The elements of the closed-loop system mode controllability matrix (controllability condition) are used to design robust closed-loop systems. The main result shows that a robust closed loop system can be obtained by choosing closed-loop eigenvalues with minimal absolute value mode controllability elements. A criterion for the selection of robust closed-loop eigenvalues is provided. This criterion assures that the desired closed-loop system has low sensitivity to the variation of feedback gain, state estimate errors, or measurement errors