Simultaneous \((C,A,B)\)-pairs for infinite-dimensional systems (Q1304691)

The authors consider the disturbance rejection problem for the infinite-dimensional system \(\dot{x}(t) = A x(t) + B u(t) + E \xi(t)\), \(y(t) = C x(t)\), \(z(t)=D x(t)\), where \(\xi\) is the disturbance, and \(z\) is the output that has to become disturbance independent. The operators in this model are unknown convex combinations of known operators, i.e., \(A= \alpha A_1 + (1-\alpha) A_2\), \(B= \beta B_1 + (1-\beta) B_2\), etc. The aim is to find a (fixed) dynamic compensator which solves the disturbance rejection problem for all \(A\)'s, \(B\)'s, \(\ldots\), and \(E\)'s. The authors use geometric theory, in particular \((C,A,B)\) pairs, to give sufficient conditions for the solvability of the problem.