Towards stochastic realization theory for Generalized Linear Switched Systems with inputs: decomposition into stochastic and deterministic components and existence and uniqueness of innovation form

Elie Rouphael; Manas Mejari; Mihaly Petreczky; Lotfi Belkoura

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arXiv · 2403.11012

Towards stochastic realization theory for Generalized Linear Switched Systems with inputs: decomposition into stochastic and deterministic components and existence and uniqueness of innovation form

Elie Rouphael·Manas Mejari·Mihaly Petreczky·Lotfi Belkoura

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Abstract

In this paper, we study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewide-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decomposition, we show existence of state-space representation in innovation form, and we provide sufficient conditions for such representations to be minimal and unique up to isomorphism.

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Elie Rouphael, Manas Mejari, Mihaly Petreczky, Lotfi Belkoura. 2024-03-16. Towards stochastic realization theory for Generalized Linear Switched Systems with inputs: decomposition into stochastic and deterministic components and existence and uniqueness of innovation form. https://arxiv.org/abs/2403.11012

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