arXiv subjects

Arya Honarpisheh

Publications and source records attributed to Arya Honarpisheh.

4 recordsLinked to original sources

arXiv2026

Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis

This paper proposes a frequency-domain estimator for low-order systems from repeated noisy measurements. The estimator minimizes a quadratic data-fitting term regularized by the nuclear norm of a Loewner matrix, subject to a convex stability constraint enforced via a semidefinite program. We prove a finite-sample error bound at the sampled frequencies and extend it to all frequencies through rational interpolation. The bound characterizes the dependence on the number of repeated experiments, number of frequency points, system order, and noise level. Numerical experiments on SISO and MIMO systems demonstrate the low-order-promoting effect of the method and validate the predicted scaling laws.

eess.SY↗

arXiv2026

Time-Varying Perturbations of Contractive Systems With an Application to Safe Stabilization

Perturbation theory for asymptotically stable systems has received sustained attention, leading to many criteria that preserve stability under uncertainty. A limitation of classical stability analysis, however, is that it is inherently equilibrium-dependent. Contractive systems, by contrast, are defined independently of any equilibrium and admit a rich set of robustness bounds. In this letter, we develop new time-varying perturbation conditions for contractive dynamics that preserve incremental exponential stability of the perturbed system and, in specific regimes, guarantee asymptotic convergence to solutions of the nominal dynamics. As an application, we propose a safety filter for steering a nominally contractive system to a desired equilibrium while avoiding an unsafe set, and we present an example illustrating advantages of the proposed method over existing approaches.

math.OC↗

arXiv2025

Generalization Error Analysis for Selective State-Space Models Through the Lens of Attention

State-space models (SSMs) have recently emerged as a compelling alternative to Transformers for sequence modeling tasks. This paper presents a theoretical generalization analysis of selective SSMs, the core architectural component behind the Mamba model. We derive a novel covering number-based generalization bound for selective SSMs, building upon recent theoretical advances in the analysis of Transformer models. Using this result, we analyze how the spectral abscissa of the continuous-time state matrix influences the model's stability during training and its ability to generalize across sequence lengths. We empirically validate our findings on a synthetic majority task, the IMDb sentiment classification benchmark, and the ListOps task, demonstrating how our theoretical insights translate into practical model behavior.

cs.LG↗

arXiv2025

Safe Control for Pursuit-Evasion with Density Functions

This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust safe control problem. Using density functions and semi-algebraic set definitions, we derive sufficient conditions for weak eventuality and evasion, reformulating the problem into a convex sum-of-squares program solvable via standard semidefinite programming solvers. This approach avoids the computational complexity of solving the Hamilton-Jacobi-Isaacs partial differential equation, offering a scalable and efficient framework. Numerical simulations demonstrate the efficacy of the proposed method.

math.OC↗