Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915728168321024 |
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| author | Jha, Dev Prakash George, Raju K. |
| author_facet | Jha, Dev Prakash George, Raju K. |
| contents | We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is introduced, which requires the state, the memory functional, and the delayed history to vanish at the terminal time. Using a duality approach, we establish an augmented observability inequality for the adjoint system and show its equivalence to controllability. In the finite-dimensional setting, this leads to sharp necessary and sufficient algebraic rank conditions extending the classical Kalman criterion to systems with memory and delay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions Jha, Dev Prakash George, Raju K. Optimization and Control We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is introduced, which requires the state, the memory functional, and the delayed history to vanish at the terminal time. Using a duality approach, we establish an augmented observability inequality for the adjoint system and show its equivalence to controllability. In the finite-dimensional setting, this leads to sharp necessary and sufficient algebraic rank conditions extending the classical Kalman criterion to systems with memory and delay. |
| title | Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.09193 |