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.
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© 1979 Springer-Verlag New York
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Wonham, W.M. (1979). Noninteracting Control III: Generic Solvability. In: Linear Multivariable Control: a Geometric Approach. Applications of Mathematics, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0068-7_12
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DOI: https://doi.org/10.1007/978-1-4684-0068-7_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0070-0
Online ISBN: 978-1-4684-0068-7
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