Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks (Q2730874)

Linear discrete control systems with two independent variables and constant coefficients are considered. It is generally assumed that the control system is given in the so-called Roesser form [\textit{T. Kaczorek}, Linear control systems, Vol. 1 and Vol 2 (1992; Zbl 0784.93002) and (1993; Zbl 0784.93003)]. Using algebraic methods, sufficient conditions under which it is possible to choose state feedbacks such that the nonzero closed-loop characteristic polynomial has degree zero are formulated and proved. This procedure of decreasing the degree of the closed-loop characteristic polynomial by state feedbacks is called the elimination of finite eigenvalues of the Roesser model of 2-D discrete control systems. A procedure for the computation of the feedback gain matrices is presented and illustrated by a numerical example. It should be pointed out that the general theory of 2-D discrete control systems can be found in the monograph [\textit{T. Kaczorek}, Two-dimensional linear systems (1985; Zbl 0593.93031)].