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arXiv · 2601.09193

Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions

Dev Prakash Jha·Raju K. George
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Abstract

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.

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Dev Prakash Jha, Raju K. George. 2026-01-14. Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions. https://arxiv.org/abs/2601.09193

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