Noninteracting Control III: Generic Solvability

Abstract

In this chapter we discuss solvability of the noninteraction problem from the viewpoint of genericity, in the parameter space of the matrices A, B, and the D _i (i ∈ k). It turns out that noninteraction is possible for almost all data sets (A, B, D₁,…, D _k ) if and only if the array dimensions of the given matrices satisfy appropriate, rather mild, constraints. When these conditions fail dec-oupling is possible, if at all, only for system structures which are rather special. Finally, in the generically solvable case we determine the generic bounds on dynamic order of a decoupling compensator, corresponding to the “naive” and “efficient” extension procedures of Chapters 9 and 10, respectively.