Spectrum assignment in linear systems with several commensurate lumped and distributed delays in state by means of static output feedback

A linear control system defined by a stationary differential equation of $n$th order with several commensurate lumped and distributed delays in state is considered. In the system, the input is a linear combination of $m$ variables and their derivatives of order not more than $n-p$ and the output is a $k$-dimensional vector of linear combinations of the state and its derivatives of order not more than $p-1$. For this system, a spectrum assignment problem by linear static output feedback with commensurate lumped and distributed delays is studied. Necessary and sufficient conditions are obtained for solvability of the arbitrary spectrum assignment problem by static output feedback controller. Corollaries on stabilization of the system are obtained.