Parameter insensitive disturbance-rejection problems with direct control and with known disturbances for infinite-dimensional systems
Consider the infinite-dimensional system of the form \(\dot x(t)= Ax(t)+ Bu(t)+ E\xi(t)\), \(y(t)= Cx(t)\), \(z(t)= Dx(t)+ Ku(t)\), where \(B\), \(C\), \(D\), \(E\), and \(K\) are unknown convex combinations of given operators, \(B_0\), \(B_1\), \(C_0\), \(C_1\), etc., and where \(A\) is an unknown multiple of a given operator. The parameter insensitive disturbance rejection problem is to design of feedback, \(u(t)= Hy(t)\) such that in the closed loop system the disturbance \(\xi\) has no influence on \(z\). The authors solve this problem using the geometric approach, i.e., they give conditions for the solvability in term of subspace inclusions. As a variation of the first problem they also consider the problem of known disturbances. For this problem a part of the disturbances is known and this part may be used in the feedback.
scientific article; zbMATH DE number 1359765
scientific article