Matrix eigenvalue spectrum assignment for linear control systems by static output feedback

Abstract For a linear time-invariant control system defined by a linear differential equation of the n-th order with a multidimensional state, input and output, we set and study the problem of arbitrary matrix eigenvalue spectrum assignment by linear static output feedback. We obtain controllability-like rank conditions that are necessary and sufficient for the problem of arbitrary matrix eigenvalue spectrum assignment and are sufficient for the problem of arbitrary eigenvalue spectrum assignment by linear static output feedback. It is proved that, in particular cases, when the system has block scalar matrix coefficients, these conditions can be relaxed. The obtained results generalize the known results for the corresponding problem by static state feedback and by static output feedback in the case of the one-dimensional equation. Examples are presented to illustrate the results.