State-feedback controllers for linear descriptor systems with singular matrix pencils (Q1363078)

Linear, finite-dimensional, continuous-time, stationary, descriptor control systems are considered. Using algebraic methods, necessary and sufficient conditions for the existence of a state feedback controller for the system with singular matrix pencil, such that all finite Jordan eigenvalues of the closed-loop system are assigned to fixed points of the complex plane, have been established. Moreover, it is possible to derive a state-feedback static controller such that the closed loop characteristic polynomial is equal to the desired one. A numerical procedure for finding a gain constant matrix is also presented. Simple illustrative numerical examples are given. The paper extends the classical state-feedback results given by \textit{T. Kaczorek} [Linear control systems, Vol. 1, and Vol. 2 (1992; Zbl 0784.93002) and (1993; Zbl 0784.93003)], for descriptor control systems with singular matrix pencil.