A Direct State-Space Realization of Discrete-Time Linear Parameter-Varying Input-Output Models
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912248395464704 |
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| author | Kon, Johan Tóth, Roland van de Wijdeven, Jeroen Heertjes, Marcel Oomen, Tom |
| author_facet | Kon, Johan Tóth, Roland van de Wijdeven, Jeroen Heertjes, Marcel Oomen, Tom |
| contents | A minimal state-space (SS) realization of an identified linear parameter-varying (LPV) input-output (IO) model usually introduces dynamic and nonlinear dependency of the state-space coefficient functions, complicating stability analysis and controller synthesis. The aim of this paper is to introduce and analyze a direct SS realization of this IO model that avoids this nonlinear and dynamic dependency, at the cost of introducing a nonminimal state. It is shown that this direct SS realization 1) is reachable under a coprimeness condition on the coefficient functions of the IO model and a well-posedness condition on the model order, and 2) is never observable but that the unobservable directions converge to zero in a finite amount of steps, i.e., that the realization is reconstructible. The derived results are illustrated through numerical examples in both the LPV and LTI case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Direct State-Space Realization of Discrete-Time Linear Parameter-Varying Input-Output Models Kon, Johan Tóth, Roland van de Wijdeven, Jeroen Heertjes, Marcel Oomen, Tom Systems and Control A minimal state-space (SS) realization of an identified linear parameter-varying (LPV) input-output (IO) model usually introduces dynamic and nonlinear dependency of the state-space coefficient functions, complicating stability analysis and controller synthesis. The aim of this paper is to introduce and analyze a direct SS realization of this IO model that avoids this nonlinear and dynamic dependency, at the cost of introducing a nonminimal state. It is shown that this direct SS realization 1) is reachable under a coprimeness condition on the coefficient functions of the IO model and a well-posedness condition on the model order, and 2) is never observable but that the unobservable directions converge to zero in a finite amount of steps, i.e., that the realization is reconstructible. The derived results are illustrated through numerical examples in both the LPV and LTI case. |
| title | A Direct State-Space Realization of Discrete-Time Linear Parameter-Varying Input-Output Models |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2502.19321 |