Block noninteracting control with (non)regular static state feedback: A complete solution

Abstract

We consider linear time-invariant systems ( C, A, B) where the output map C is partitioned into k blocks C i . We assume that the system are block right invertible, i.e. the rank of ( C, A, B) equals the sum of the ranks of the subsystems ( C i , A, B). We give, for the first time, a necessary and sufficient condition for the solution of the block decoupling problem using static state feedbacks of the type u = Fx + Gv, with G possibly nonregular; for solving the decoupling problem we impose that the rank of the closed-loop system equals that of ( C, A, B). This is a structural condition in terms of invariant lists of integers: the infinite zero orders, the block essential orders and Morse's list I 2 of ( C, A, B). The main result (Theorem 3) generalizes that of our previous work for the so called Morgan's Problem, i.e. the row by row decoupling problem.