On solutions and algebraic duality of generalised linear discrete time systems
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I. K. Dassios
Abstract
We study a class of generalised linear discrete time systems whose coefficients are square constant matrices. The main objective of this research is to provide a link between the solutions of a class of singular linear discrete time systems and their proper (and transposed) dual systems. First, we study the prime system and by using the invariants of its matrix pencil we give necessary and sufficient conditions for existence and uniqueness of solutions, and obtain formulas for the solutions. Next, we prove that by using the same matrix pencil we can study the existence and uniqueness of solutions of the proper and transposed dual system. Moreover their solutions, when they exist, can be explicitly represented without resorting to further processes of computations for each one separately. Finally, we provide a numerical example to justify the theory.
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- On the algebras of almost minimal rank
- Definition of positively closed classes by endomorphism semigroups
- The power conjugacy search problem in a cyclic subgroup in groups with the condition C.3/ & T.6/
- Lawvere intervals and the Möbius function of a Möbius category
- On algorithmic solvability of the A-completeness problem for systems of boundedly determinate functions containing all one-place boundedly determinate S-functions
- On uniqueness of alphabetic decoding
- On unstable branching graphs
- Extremal sets of graphs in the problem of demarcation in the family of hereditary closed classes of graphs
- Statistical problems on random permutations with censored data
- On large deviations of branching processes in a random environment with arbitrary initial number of particles: critical and supercritical cases
- Multitype branching processes evolving in a Markovian environment
- On solutions and algebraic duality of generalised linear discrete time systems
- On the number of Gram’s intervals containing the ordinates of successive zeros of the Riemann zeta function
