BLOCK NONINTERACTING CONTROL WITH (NON)REGULAR STATIC STATE FEEDBACK - A COMPLETE SOLUTION

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 I2 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.