Article
Engineering, Electrical & Electronic
Yufeng Tian, Zhanshan Wang
Summary: This study presents an improved solution to the problem of H-infinity performance state estimation for static neural networks with time-varying delays. By deriving a less conservative criterion and designing estimator gain matrices independent of activation function, the effectiveness of the estimation method has been improved. This approach eliminates the constraint of having invertible activation functions, as compared to existing works.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Mathematics, Applied
Yufeng Tian, Zhanshan Wang
Summary: This paper explores the H-infinity performance state estimation problem for static neural networks with time-varying delays. A new criterion is proposed by combining a parameter-dependent reciprocally convex inequality and an improved Lyapunov-Krasovskii functional, leading to improved performance and stability of the estimator. The study overcomes restrictions on slack matrices and demonstrates advantages through two examples.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Artificial Intelligence
Chenyang Shi, Kachon Hoi, Seakweng Vong
Summary: This paper studies the stability of a neural network with time-varying delay. Two general inequalities with two and three terms are derived to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). The LKF method is used to develop a stability criterion for time-delay neural networks by using these new inequalities. Numerical results are provided to demonstrate the improvement of the new criterion.
Article
Computer Science, Artificial Intelligence
Guoqiang Tan, Zhanshan Wang
Summary: This paper proposes a method for estimating the reachable set of delayed Markovian jump neural networks with bounded disturbances. By using an improved inequality and an augmented Lyapunov-Krasovskii functional, an accurate ellipsoidal description of the reachable set is obtained, and the effectiveness of the method is demonstrated through simulation results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Automation & Control Systems
Yufeng Tian, Yuzhong Wang, Junchao Ren
Summary: This article focuses on the event-triggered H-infinity state estimation problem of delayed neural networks. A new event-triggered scheme is designed to balance the performance of the state estimator and network communication bandwidth. Additionally, an auxiliary function-type free-matrix-based integral inequality is proposed to establish conditions for the estimation error system to be stable and satisfy H-infinity performance.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Mathematics, Applied
Liangliang Guo, Yali Dong
Summary: This paper investigates the robust exponential stabilization of delayed neural networks with parameter uncertainties and external disturbance. The delay dependent state feedback controller is designed and appropriate stability criteria are obtained. The controller gain matrices can be obtained by solving linear matrix inequalities. Three simulation examples are provided to demonstrate the effectiveness of the proposed methods.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Yibo Wang, Changchun Hua, PooGyeon Park, Cheng Qian
Summary: This paper investigates the stability analysis issue of time-varying delay systems by proposing a novel reciprocally convex inequality lemma (RCIL). A new reciprocally convex combination method is introduced using a matrix-valued polynomial, which includes some previous methods as special examples. A newly asymmetric Lyapunov-Krasovskii (L-K) functional is presented by introducing delay-product terms, providing additional delay convexity information. The proposed L-K functional and RCIL are combined to develop new stability conditions. Numerical examples and simulation experiments demonstrate the advancement of the proposed method.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
Yufeng Tian, Zhanshan Wang
Summary: This paper investigates extended dissipative state estimation for static neural networks with time varying delays, introducing a new DPT functional and a PDRCI inequality to tighten the bounds. The estimator design condition ensures asymptotic stability and dissipativity, with gain matrices solved using LMIs. Flexibility of estimator solutions is increased by overcoming restrictions on slack matrices, as demonstrated with an example.
Article
Mathematics, Applied
Qiao Chen, Xinge Liu, Peiyu Guo, Hua Liu, Xiayun Li
Summary: This paper investigates the problems of stability and H-infinity performance for discrete-time neural networks with time-varying delay, in order to develop a less conservative delay-dependent stability criterion and method for H-infinity performance analysis. By proving an improved reciprocally convex inequality and deriving a novel free-matrix-based summation inequality, two improved sufficient conditions for stability and H-infinity performance of discrete-time neural networks with time-varying delay are obtained in terms of linear matrix inequalities (LMIs).
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Guoqiang Tan, Zhanshan Wang
Summary: This paper introduces a new method to study the stability and dissipativity of neural networks with time-varying delay, obtaining sufficient conditions through a novel reciprocally convex inequality, and validating the effectiveness of the method through simulations.
Article
Mathematics, Applied
Zerong Ren, Junkang Tian
Summary: This paper introduces an improved reciprocally convex inequality and obtains a new stability criterion in terms of linear matrix inequalities. The effectiveness of the method is demonstrated through two numerical examples.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Automation & Control Systems
Jun Chen, Ju H. Park, Shengyuan Xu
Summary: This paper addresses the stability problem of linear systems with time-varying delay using the Lyapunov-Krasovskii (L-K) functional method. It develops an a-polynomial reciprocally convex combination lemma (RCCL) with an undetermined parameter m, extends the necessary and sufficient negative-definiteness condition and quadratic-partitioning method to the general case with a non-zero lower bound of the time-varying interval, and derives relaxed stability criteria based on these techniques. Numerical examples are provided to demonstrate the improvement and effectiveness of the proposed approach.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Wei Qian, Hang Shi, Zhonghua Wu, Yunji Zhao
Summary: This dissertation focuses on the H-infinity state estimation for static neural networks with time-varying delays. A novel Lyapunov-Krasovskii (L-K) functional is developed to fully utilize delay information, incorporating delay-product-type (DPT) terms in both the non-integral and single integral functionals, along with the introduction of an S-dependent integral term combined with the single integral DPT functional for the first time. To reduce conservatism, generalized free-weighting-matrix integral inequality and other methods are employed with the proposed L-K functional. Additionally, a general gain inverse solution is provided, resulting in a gain matrix independent of the activation function, eliminating the requirement of reversibility for the activation function. Numerical examples are presented to demonstrate the advantages of the proposed approach.
Article
Mathematics, Applied
Wei Qian, Haibo Liu, Yunji Zhao, Yalong Li
Summary: This dissertation investigates the Hoc and state estimation issue of neural networks with hybrid delays, and proposes a more general system model and state estimator. By introducing the innovative Lyapunov-Krasovskii functional and the generalized free-weighting-matrix integral inequality, less conservative criteria are obtained, and the advantages of the achieved approach are demonstrated through two simulated examples.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Information Systems
Xue-Jun Pan, Bin Yang, Jun-Jun Cao, Xu-Dong Zhao
Summary: This paper investigates stability analysis of Takagi-Sugeno (T-S) fuzzy systems with time-varying delays by introducing an extended delay-dependent reciprocally convex inequality and proposing an improved stability criteria using augmented Lyapunov-Krasovskii functional. Several numerical examples are provided to illustrate the advantages and effectiveness of the proposed criteria by comparing the maximum delay bounds.
INFORMATION SCIENCES
(2021)
Article
Engineering, Electrical & Electronic
Guoqiang Tan, Zhanshan Wang
Summary: This brief introduces a method for generalized dissipativity state estimation for static neural networks, utilizing an improved convex inequality and a PI estimator. Simulation results demonstrate the superior performance and advantages of the proposed method over existing ones.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Engineering, Electrical & Electronic
Guoqiang Tan, Zhan Shi, Pipi Liu, Zhanshan Wang
Summary: This paper presents a robust H-infinity load frequency control method for power systems with two time delays in the presence of load disturbance. By proposing an improved reciprocally convex inequality and deriving a less conservative criterion, an algorithm is provided to effectively convert the coupled nonlinear terms into linear items, without solving the inverse of the matrix with row full rank. Simulations confirm the superiority of the presented method.
INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS
(2021)
Article
Computer Science, Artificial Intelligence
Guoqiang Tan, Zhanshan Wang
Summary: This paper introduces a new method to study the stability and dissipativity of neural networks with time-varying delay, obtaining sufficient conditions through a novel reciprocally convex inequality, and validating the effectiveness of the method through simulations.
Article
Mathematics, Applied
Guoqiang Tan, Zhanshan Wang
Summary: This paper proposes a delay-product-type integral inequality for stability analysis of systems with time-varying delay. An augmented Lyapunov-Krasovskii functional is tailored to consider more information about the instant state and the delayed states. The derived conditions for stability are less conservative.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Guoqiang Tan, Zhanshan Wang
Summary: This paper proposes a method for estimating the reachable set of delayed Markovian jump neural networks with bounded disturbances. By using an improved inequality and an augmented Lyapunov-Krasovskii functional, an accurate ellipsoidal description of the reachable set is obtained, and the effectiveness of the method is demonstrated through simulation results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Guoqiang Tan, Zhanshan Wang, Zhan Shi
Summary: This brief investigates the problem of state estimation for quaternion-valued neural networks (QVNNs) with time-varying delays. An extended Jensen inequality with a quaternion term is derived by extending the Jensen inequality to the quaternion domain. A class of proportional-integral state estimator (PISE) with an exponential decay term is proposed. By constructing a suitable Lyapunov-Krasovskii functional (LKF), sufficient conditions are obtained to ensure the existence of the designed PISE and the gain matrices of the designed PISE can be directly computed. Simulations are provided to illustrate the advantages of the proposed method.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Guoqiang Tan, Zhanshan Wang
Summary: This paper investigates the stability problem of recurrent neural networks (RNNs) with time-varying delay. A flexible negative-determination quadratic function method is proposed by introducing some flexibility factors, which contains existing methods and has less conservatism. Integral inequalities and the flexible negative-determination quadratic function method are then used to provide an accurate upper bound of the Lyapunov-Krasovskii functional (LKF) derivative. As a result, a less conservative stability criterion for delayed RNNs is derived, and its effectiveness and superiority are illustrated through numerical examples.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
