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Simultaneous stabilization in A ( )

Raymond Mortini, Brett D. Wick (2009)

Studia Mathematica

We study the problem of simultaneous stabilization for the algebra A ( ) . Invertible pairs ( f j , g j ) , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that α f j + β g j is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since A ( ) has stable rank two, we are faced here with a different situation....

Stabilizability of multi-agent systems over finite fields via fully actuated system approaches

Yunsi Yang, Jun-e Feng, Lei Jia (2025)

Kybernetika

The problem of stabilizability of high-order fully actuated (HOFA) multi-agent systems over finite fields is considered in this paper. The necessary and sufficient conditions for the stabilizability of HOFA multi-agent systems are presented, which indicates the stabilizability is closely related to the interaction topology among agents. Using the full-actuation property of HOFA models, a stabilization control protocol with neighbor interaction is given for HOFA multi-agent systems. Additionally,...

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