This paper presents a systematic study on the modeling and stability analysis of fractional-order cascaded RLC networks with time delays. A generalized model of an $n$-stage cascaded RLC network with time delays is developed using the Caputo fractional derivative. The corresponding fractional-order differential equations are derived for both single-stage ($n=1$) and two-stage ($n=2$) configurations. The transcendental characteristic equation of the system is obtained via Laplace transform. By applying the Matignon stability criterion, asymptotic stability conditions are established for systems with and without time delays. It is shown that stability in the delay-free case depends mainly on the fractional order $\alpha$, whereas in the presence of time delays, stability is independent of $\alpha$ and instead governed by the delay parameter $\tau$. Notably, the critical delay threshold $\tau_{\mathrm{max}}$ for system stability is derived analytically. A detailed numerical study (Table I) further elucidates the effects of key parameters, including the resistance $R$, inductance $L$, capacitance $C$, fractional order $\alpha$, and time delay $\tau$ on the stability behavior.

This study provides a theoretical basis and practical design guidelines for tuning parameters to ensure stability in fractional-order circuits with time delays.

In this paper, we utilize the theory of Kurzweil-Henstock integrals to investigate new criteria

for boundedness in terms of two measures for generalized ordinary differential equations.

As applications, we establish criteria for $(h_{0}, h)$-uniform boundedness

and $(h_{0}, h)$-uniform ultimate boundedness in terms of two measures for impulsive differential equations.

In various imaging applications such as autonomous vehicles and drones, autofocus lenses are indispensable for capturing clear images. However, conventional camera calibration methods typically rely either on processing multiple images at a fixed focal length or on detecting multi-plane markers in a single image and then applying multi-image calibration models. This paper proposes a flexible and accurate calibration approach that extracts subpixel saddle points from a single image containing three non-coplanar calibration boards. To compute accurate homography matrices for the three boards, outliers are removed by eliminating chessboard points that deviated from the fitted grid lines according to their row and column positions. Initial estimates of the intrinsic parameters and the poses of the three planar chessboards are obtained using the three homography matrices in combination with Zhang's calibration method.

During parameter refinement, a multi-objective optimization function is constructed, incorporating three error terms:

(1) Reprojection error of the inlier grid points;

(2) Mechanism-driven error derived from the relationship between homography matrices and camera parameters;

(3) Cross-planar linearity constraint error, which preserves the pre-imaging collinearity of any five points across different planes after projection.

For weight selection in the optimization process, confidence intervals of the detected grid points are analyzed by horizontally rotating the reprojection lines to reduce bias introduced by line slope. The optimal weights are determined by minimizing the number of points whose confidence intervals does not intersect the reprojected lines. When multiple candidates yield similar reprojection performance, the parameter set with the smallest reprojection error is selected as the final result. This method efficiently estimates both intrinsic and extrinsic camera parameters. Simulations and real-world experiments validate the high precision and effectiveness of the proposed approach. Our technique is straightforward, practical, and holds significant theoretical and practical value for rapid and reliable camera calibration.