Thermal Visual Place Recognition (Thermal VPR) maps camera observations to metric poses within a mapped environment, serving as a prerequisite for autonomous navigation. However, thermal VPR suffers from severe environmental dependence, heavy online retraining overheads, and an inability to model dynamic non-linear shifts, causing existing frameworks to fail during online deployment. To achieve robust domain-invariant place recognition, we bridge Analytic Class-Incremental Learning (ACIL) with domain-invariant VPR for the first time, revealing that its gradient-free matrix updates construct a surprisingly strong baseline that outperforms conventional fine-tuning. Nevertheless, standard ACIL exhibits a critical vulnerability to extreme non-linear thermal fluctuations due to its structural linear assumptions. To overcome this limitation, we exploit a novel algebraic equivalence between ACIL and modern control theory, proposing a framework which embeds Unscented propagation (U-ACIL), Gaussian Mixture partitioning (GMM-ACIL), and minimax $H_\infty$ optimization ($H_\infty$-ACIL) directly into the update loop. Our formulation guarantees exact closed-form matrix updates within $\mathcal{O}(1)$ computational complexity, bypassing backpropagation to ensure that the online update latency ($Δt_{\mathrm{learn}}$) remains strictly bounded below the sensor acquisition interval ($Δt_{\mathrm{acquire}}$), thereby eliminating trajectory jumps in real-time SLAM pipelines.

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