On eigensystem assignment with output feedback

A new approach for the eigenvalue assignment of linear, first-order, time-invariant systems using output feedback is developed. The approach can assign the maximum allowable number of closed-loop eigenvalues through output feedback provided that the system is fully controllable and observable, and both the input influence and output influence matrices are full rank. First, a collection of bases for the space of attainable closed-loop eigenvectors is generated using the Singular Value Decomposition or QR Decomposition techniques. Then, an algorithm based on subspace intersections is developed and used to compute the corresponding coefficients of the bases, and the required output feedback gain matrix. Moreover, the additional freedom provided by the multi-inputs and multi-outputs beyond the eigenvalue assignment is characterized for possible exploitation. A numerical example is given to demonstrate the viability of the proposed approach.