Restrictions on attainable poles and methods for pole assignment with output feedback

The paper establishes the restrictions on the attainable closed-loop poles in single-input systems when constant feedback is employed from an output vector of smaller dimension than the state vector. These restrictions are linear equations in the coefficients of the closed-loop characteristic polynomial, and are obtained from the matrices describing the system in the state-space form. The closed-loop pole specifications are then expressed as linear equations in the coefficients of the characteristic polynomial, and these are solved simultaneously with the constraint equation to obtain the output-feedback vector required for pole assignment. The results developed for single-input systems are then extended to multivariable systems where the output-feedback matrices used are restricted to have unity rank. Further, arbitrary pole assignment in multivariable systems using unity-rank output feedback is studied. A number of illustrative examples are given.