This paper presents a novel variable matrix-type step-size affine projection sign algorithm (VMSS-APSA) characterized by robustness against impulsive noise. To mathematically derive a matrix-type step size, VMSS-APSA utilizes mean-square deviation (MSD) for the modified version of the original APSA. Accurately establishing the MSD of APSA is impossible. Therefore, the proposed VMSS-APSA derives the upper bound of the MSD using the upper bound of the ${\mathcal{L}}_1$-norm of the measurement noise. The optimal matrix-type step size is calculated at each iteration by minimizing the upper bound of the MSD, thereby improving the filter performance in terms of convergence rate and steady-state estimation error. Because a novel cost function of the proposed VMSS-APSA was designed to maintain a form similar to the original APSA, they have symmetric characteristics. Simulation results demonstrate that the proposed VMSS-APSA improves filter performance in a system-identification scenario in the presence of impulsive noise.

Herein, we propose a normalized subband adaptive filter (NSAF) algorithm that adjusts both the step size and regularization parameter. Based on the random-walk model, the proposed algorithm is derived by minimizing the mean-square deviation of the NSAF at each iteration to calculate the optimal parameters. We also propose a method for estimating the uncertainty in an unknown system. Consequently, the proposed algorithm improves performance in terms of tracking speed and misalignment. Simulation results show that the proposed NSAF outperforms existing algorithms in system identification scenarios.

In this paper, we propose a novel normalized least mean squares (NLMS) algorithm for system identification applications. Our approach involves analyzing the mean squared deviation performance of the NLMS algorithm using a random walk model to select two optimal parameters, the step size and regularization parameters, for the rapid convergence of the colored input signals. We verified that the proposed algorithm exhibited faster convergence than existing algorithms, even in scenarios of sudden system changes.

This study addresses the stabilization condition for Markovian jump systems with quantized input and generally uncertain transition rates. To stabilize Markovian jump systems with nonlinear inputs using only partial knowledge regarding to the transition rates, the proposed controller is designed as two control parts: a linear control part for stabilizing the system and a nonlinear control part for eliminating undesirable effects from the quantized input. Moreover, an appropriate weighting method, using lower and upper bounds of the partial transition rate, is employed to derive a less conservative stability condition. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed controller.

최근 시간 지연 시스템의 안정성 해석을 위해 affine Bessel-Legendre(BL) 부등식이 제안되었다. 제안된 부등식의 차수를 높일수록 더 큰 시간 지연에 대해 안정성을 판별할 수 있는 보다 덜 보수적인 시간 지연 시스템의 안정성 조건을 얻을 수 있지만, 이를 위해서는 차수의 변경에 따른 새로운 Lyapunov-Krasovskii functional의 설계와 이를 처리하기 위한 기법이 요구된다. 본 논문에서는 affine BL 부등식의 차수에 따른 일반화 된 Lyapunov-Krasovskii functional과, 이에 기반한 일반화 된 시간 지연 시스템의 안정성 조건을 제안한다. 제안하는 방법을 활용하면 다양한 부등식의 차수에 따른 안정성 조건을 보다 쉽게 구할 수 있다. 수치 예제의 결과를 통해 제안하는 방법의 일반성과 효율성을 입증한다.