Block Decoupling for Linear Systems over Unique Factorization Domains

Unique Factorization Monoids and Domains

It is the purpose of this paper to construct unique factorization (uf) monoids and domains. The principal results are: (1) The free product of a well-ordered set of monoids is a uf-monoid iff every monoid in the set is a uf-monoid. (2) If M is an ordered monoid and F is a field, the ring ^[[iW"]] of all formal power series with well-ordered support is a uf-domain iff M is naturally ordered (i.e...

Lectures On Unique Factorization Domains

Unique Factorization in Integral Domains

Throughout R is an integral domain unless otherwise specified. Let A and B be sets. We use the notation A ⊆ B to indicate that A is a subset of B and we use the notation A ⊂ B to mean that A is a proper subset of B. The group of elements in R which have a multiplicative inverse (the group of units of R) is denoted R×. Since R has no zero divisors cancellation holds. If a, b, c ∈ R and a 6= 0 th...

Input-output block decoupling of linear time-varying singular systems

The input–output block decoupling problem by state feedback is studied for linear time-varying singular systems. First, an algorithm, the regularization algorithm, is developed such that the system can be made by state feedback to have a unique impulse-free solution. Second, another algorithm, the block decoupling algorithm, is proposed, which provides sufficient conditions for the solvability ...

Block-decoupling linear multivariable systems: necessary and sufficient conditions

We study block decoupling of linear multivariable systems under unity-feedback configuration. We consider plants which have unstable pole-zero coincidences and give necessary and sufficient conditions for the existence of the block decoupling controllers. The conditions are particularly simple for plants with only simple unstable pole-zero coincidences. An illustrative example is given.