Partial Pole Placement and Controller Norm Optimization Over Polynomial Stability Region

An arbitrary subset (n − m) of the n closed loop eigenvalues of an n order continuous time single input linear time invariant (LTI) system is to be placed using full state feedback, at pre-specified locations in the complex plane. The remaining m closed loop eigenvalues can be placed anywhere inside a pre-defined region in the complex plane. This region constraint on the unspecified poles is translated into an ellipsoidal constraint on the characteristic polynomial coefficients through a convex inner approximation for polynomial stability regions. The closed loop locations for thesem eigenvalues are chosen through an explicit minimization of the feedback gain vector norm leading to an efficiently solvable semidefinite program. The required controller effort is thus minimized leading to less expensive actuators.