BEYOND THE GIVONE-ROESSER/FORNASINI-MARCHESINI MODELS: A UNIVERSAL INPUT/STATE/OUTPUT MODEL FOR 2-D SYSTEMS

• Tipo: Artigo em Revista Científica Internacional
• Data: 2025

Autores

Debasattam Pal (Autor) Outra; Eva Zerz (Autor) Outra; Rocha, P (Autor) FEUP

Revista

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Título: MATHEMATICAL CONTROL AND RELATED FIELDS

Vol. 0

Páginas: 0-0

ISSN: 2156-8472

Indexação

ISI Web of Knowledge - 0 Citações

Outras Informações

ID Authenticus: P-01A-2P6

DOI: 10.3934/mcrf.2025048

Abstract (EN): Regardless of their widespread popularity, the Givone-Roesser and the Fornasini-Marchesini models are known to be incapable of representing a huge class of 2-D systems [11]. In this paper, we provide a method to construct a state space (input/state/output) representation from a given higher order representation of an arbitrary 2-D system. A crucial role is played by a normalization process - based on a suitable linear change of coordinates on the indexing set - that changes the system's equations to a useful form. The continuous version of this process is the classical result from algebraic geometry called Noether's normalization lemma; an extension of the same to the discrete case was done in [13]. Using this normalization, called Noether normalization, we first provide a method of obtaining an input/state/output (i/s/o) representation of a given controllable 2-D system. Then we do the same for autonomous systems. Finally, we use the notion of decomposing a general uncontrollable system as a sum of its controllable part and an autonomous subsystem to obtain an i/s/o representation for the general uncontrollable 2-D system. A key issue that we solve in this decomposition based approach is that of the existence of a Noether normalization that simultaneously normalizes the controllable and autonomous subsystems.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 18