On Differential Controllability and Observability Functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913776173842432 |
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| author | Kawano, Yu Besselink, Bart Scherpen, Jacquelien M. A. |
| author_facet | Kawano, Yu Besselink, Bart Scherpen, Jacquelien M. A. |
| contents | Differential balancing theory for nonlinear model reduction relies on differential controllability and observability functions. In this paper, we further investigate them from two different perspectives. First, we establish novel connections between these differential energy functions and their incremental counterparts by assuming the existence of the corresponding optimal state feedback for each controllability function. Specifically, an upper bound on the incremental controllability/observability function is provided by the corresponding differential energy function. Conversely, an upper bound on the differential controllability function can be estimated from the incremental controllability function. Furthermore, the differential observability function can be constructed from the incremental observability function. Second, we explore the positive definiteness of the differential controllability/observability function in the context of controllability/observability and stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Differential Controllability and Observability Functions Kawano, Yu Besselink, Bart Scherpen, Jacquelien M. A. Systems and Control Differential balancing theory for nonlinear model reduction relies on differential controllability and observability functions. In this paper, we further investigate them from two different perspectives. First, we establish novel connections between these differential energy functions and their incremental counterparts by assuming the existence of the corresponding optimal state feedback for each controllability function. Specifically, an upper bound on the incremental controllability/observability function is provided by the corresponding differential energy function. Conversely, an upper bound on the differential controllability function can be estimated from the incremental controllability function. Furthermore, the differential observability function can be constructed from the incremental observability function. Second, we explore the positive definiteness of the differential controllability/observability function in the context of controllability/observability and stability. |
| title | On Differential Controllability and Observability Functions |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2504.03250 |