This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

The problem of estimating a large covariance matrix arises in various statistical applications. This paper develops new covariance matrix estimators based on shrinkage regularization. Individually, we consider two kinds of Toeplitz-structured target matrices as the data come from the complex Gaussian distribution. We derive the optimal tuning parameter under the mean squared error criterion in closed form by discovering the mathematical properties of the two target matrices. We get some vital moment properties of the complex Wishart distribution, then simplify the optimal tuning parameter. By unbiasedly estimating the unknown scalar quantities involved in the optimal tuning parameter, we propose two shrinkage estimators available in the large-dimensional setting. For verifying the performance of the proposed covariance matrix estimators, we provide some numerical simulations and applications to array signal processing compared to some existing estimators.

Estimating a covariance matrix plays an essential role in modern statistics and practical applications. One key challenge is seeking an outperformed covariance matrix estimator in large dimension and small sample size scenarios. In this paper, we develop new covariance matrix estimators based on shrinkage regularization acclaimed in high-dimensional statistics. Individually, we consider two kinds of Toeplitz-structured target matrices in the shrinkage estimation. Firstly, we obtain the optimal tuning parameter under the mean squared error criterion in closed form by discovering the mathematical properties of the two target matrices. Secondly, we get some vital moment properties of the complex Wishart distribution, and then we simplify the optimal tuning parameter as the data come from the complex Gaussian distribution. Thirdly, we unbiasedly estimate the unknown scalars involved in the optimal tuning parameter. Then we immediately propose available shrinkage estimators. To verify the performance of the proposed covariance matrix estimators, we provide some numerical simulations and applications to array signal processing compared to some existing estimators.

1. Two-dimensional (2-D) systems have long been a basic topic in multi-dimensional system theory, since they describe coupled evolution along two independent directions and naturally arise in many ...