Stabilization of polynomially parametrized families of linear systems. The single-input case
The authors consider systems of the form \((1)\quad \dot x=A(p)x+b(p)u\) with n-dimensional state x and scalar control u. The matrix A and the vector b depend on an r-dimensional parameter p. Roughly speaking, the question is investigated of finding controls of the form \(u=k(p)x\) such that the closed-loop system is asymptotically stable, i.e. that the matrix \(A(p)+b(p)k(p)\) has all its eigenvalues in the left half plane. By using the Hurwitz stability test the authors show that the problem has a solution if and only if system (1) is controllable for each p. The treatment of this problem, which has also practical interest, is theoretic in nature. The well readable paper will be of interest primarily to those interested in various aspects of system theory.
scientific article; zbMATH DE number 3865108