Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions
Optimization and Control
2026-01-15 v1
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.
Cite
@article{arxiv.2601.09193,
title = {Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions},
author = {Dev Prakash Jha and Raju K. George},
journal= {arXiv preprint arXiv:2601.09193},
year = {2026}
}