Towards stochastic realization theory for Generalized Linear Switched Systems with inputs: decomposition into stochastic and deterministic components and existence and uniqueness of innovation form
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916163386081280 |
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| author | Rouphael, Elie Mejari, Manas Petreczky, Mihaly Belkoura, Lotfi |
| author_facet | Rouphael, Elie Mejari, Manas Petreczky, Mihaly Belkoura, Lotfi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards stochastic realization theory for Generalized Linear Switched Systems with inputs: decomposition into stochastic and deterministic components and existence and uniqueness of innovation form Rouphael, Elie Mejari, Manas Petreczky, Mihaly Belkoura, Lotfi Optimization and Control 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. |
| title | Towards stochastic realization theory for Generalized Linear Switched Systems with inputs: decomposition into stochastic and deterministic components and existence and uniqueness of innovation form |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.11012 |