This study presents a nonlinear dynamic analysis of functionally graded (FG) Triply Periodic Minimal Surface (TPMS) double-curved panels under various excitation conditions. The TPMS structures, characterized by their complex geometry and favorable strength-to-weight ratio, are increasingly used in advanced engineering applications. Using time-domain and phase-space analysis, the influence of structural parameters and excitation frequencies on the transverse displacement and velocity responses of the FG-TPMS panels was examined. Results reveal that modifications in the excitation frequency significantly affect the panels' vibrational behavior, leading to complex oscillatory patterns and nonlinear phase trajectories. This study introduces the SVM-DNN-RF algorithm, a hybrid model combining Support Vector Machine (SVM), Deep Neural Network (DNN), and Random Forest (RF) techniques to predict nonlinear dynamic behaviors from mathematically simulated datasets. By leveraging the strengths of each model—SVM's classification accuracy, DNN's deep feature extraction, and RF's robustness—the proposed algorithm achieves high predictive accuracy and generalization in capturing complex nonlinear dynamics. Results demonstrate that SVM-DNN-RF effectively handles nonlinear relationships and improves predictive performance compared to standalone models. This approach offers a powerful tool for applications requiring precise dynamic analysis, such as structural engineering, physics simulations, and complex system modeling. This complexity highlights the sensitivity of FG-TPMS panels to design and operational parameters, providing insight into optimizing these structures for improved resonance control and damping in applications requiring lightweight yet strong materials. These findings contribute to the design of advanced structural systems with tailored dynamic properties.

This paper is aimed at stabilising control for impulsive systems via the state feedback. Firstly, stability analysis for the closed-loop system is conducted using a Lyapunov-like functional (LLK) that is not necessarily continuous nor positive definite. Built on two subintervals of the impulsive interval being separated by the current instant, a concrete LLK is constructed by introducing multiple integrals of the state and cross terms among the integrals, the state and impulsive states. Integral equations of the impulsive system are exploited and high-order integral inequalities are taken when estimating the derivative of the LLK. New stability results with interval dwell-time, maximal dwell-time or minimal dwell-time are obtained. Secondly, based on the stability results the stabilising control problem is solved via linear matrix inequality approach. Finally, numerical examples illustrate that the stability results are less conservative and the control for impulsive systems is valid.

This paper is concerned with the dynamic event-triggered H ∞ filtering for networked systems with stochastic cyber attacks and quantization. First, a new dynamic event-triggered scheme is employed to save limited system resources by using a new triggering error, which includes the conventional one. Second, the filtering error system is formulated under the dynamic event-triggered scheme, quantization and stochastic cyber attacks in a unified framework, and independent Bernoulli distributed variables are used to describe the randomly occurring cyber attacks. Third, a new sufficient condition is established to guarantee the filtering error system is mean-square asymptotically stable and achieves a prescribed H ∞ performance. Under the condition, a new filter design method is given by applying a reversible linear transformation. Finally, a mechanical system with two masses and two springs is given to demonstrate the proposed method is more effective.

This paper is concerned with stability for networked control systems with a transmission delay and data packet dropouts. A hybrid model is formulated for the networked control systems to separate the constant delay and data packet dropouts, and a stability theorem is established for the hybrid model. Based on the stability theorem, a Lyapunov-Krasovskii functional plus (LKFP) approach is proposed to revolutionize the normal Lyapunov-Krasovskii functional approach. By fully employing the system information to construct an LKFP and by exploiting integral equations of the hybrid model to deal with the derivative of the LKFP, new stability results are obtained. Finally, numerical examples illustrate that the stability results are of less conservatism than some existing ones.

This paper investigates the dwell-time stability for impulsive systems by employing a Lyapunov-like functional that is time-varying, discontinuous, and not imposed to be definite positive. Employing the system information on the impulsive interval wholly rather than partly, a concrete Lyapunov-like functional is constructed, which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the impulsive state. To take advantage of the integral of the system state, integral equations of the impulsive system are explored when estimating the derivative of the extended functional. By the Lyapunov-like functional theory, new dwell-time dependent stability results with ranged dwell-time, maximal dwell-time and minimal dwell-time are derived for periodic or aperiodic impulsive systems. The stability results have less conservatism than some existing ones, which is illustrated by numerical examples.

This article is concerned with robust stability for linear impulsive delay systems with polytope uncertainties. For the linear impulsive delay systems without uncertainties, the stability is addressed by employing a Lyapunov‐Krasovskii‐like functional, which is comprised of a Lyapunov‐Krasovskii functional and an auxiliary functional. By introducing integrals of the state, an augmented Lyapunov‐Krasovskii‐like functional is constructed. With an integral inequality proposed to deal with the derivative of the Lyapunov‐Krasovskii‐like functional, a stability criterion is derived for the impulsive delay system. Then the stability criterion is extended to linear impulsive delay systems with polytope uncertainties, and a robust stability criterion is obtained. Examples are given to illustrate the stability results are valid or of less conservatism than some existing ones.

This paper is concerned with decentralized event-triggered H-infinity networked control for neural networks (NNs) subject to two types of stochastic cyber-attacks. Firstly, a new dynamic event-triggered scheme is introduced to monitor the sampled data transmissions, and two independent Bernoulli distributed variables are used to describe the randomly occurring cyber-attacks. Secondly, based on the networked control, the closed-loop system is constructed under the stochastic cyber-attacks and limited network bandwidth. Thirdly, by the Lyapunov-Krasovskii functional (LKF) approach, an improved stability criterion is established to ensure the closed-loop system is mean-square asymptotical stability with a prescribed H-infinity performance. Based on the criterion, desired control gain is determined. Finally, the effectiveness of the obtained result is illustrated by two numerical examples. (C) 2020 Elsevier Inc. All rights reserved.

This paper investigates the dwell-time dependent stability for impulsive systems by employing a new Lyapunov-like functional that is of the second order in time t. In contrary to those built on [tk, t], a part of the impulsive interval [tk,tk+1], the Lyapunov-like functional is two-sided in the sense of employing the system information on [t,tk+1] as well as [tk, t]. To deal with the derivative of the two-sided Lyapunov-like functional, which involves integrals of the state and integrals coupled by [t,tk+1] and [tk, t], integral equations of the impulsive systems are introduced and an advanced inequality is employed. By the Lyapunov-like functional theory, new dwell-time dependent stability results with ranged dwell-time, maximal dwell-time and minimal dwell-time are derived for periodic or aperiodic impulsive systems. The stability results turn out to be less conservative than some existing ones, which is illustrated by numerical examples.

This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent,and not imposed to be definite positive.Based on the system information on the sampling interval wholly rather than partly,a new Lyapunovlike functional is constructed,which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state.To take advantage of the integral of the system state,integral equations of the sampled-data system are explored when estimating the derivative of the extended functional.By the Lyapunov-like functional theory,a new sampling dependent stability result is obtained for sampled-data systems without uncertainties.Then,the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived.At last,numerical examples are given to illustrate that the stability results improve over some existing ones.

This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.

This paper is concerned with a new Lyapunov–Krasovskii functional (LKF) approach to delay-dependent stability for generalized neural networks with time-varying delays (DNN). A new LKF is constructed by employing more information of the DNN. The state, the activation function and their ramifications are introduced, and more cross terms of the activation function and their ramifications are included in the LKF. Moreover, the new LKF also makes best of the characteristic of the activation function. On the other hand, when estimating the derivative of the LKF, we take advantages of some equations and inequalities that reveal the relationship among the state, the activation function and their ramifications, employ advanced inequalities to deal with integrals arising from the derivative of the LKF, thus resulting in a tight upper bound of the derivative of the LKF. By checking the negative definiteness of the upper bound that is a quadratic function in the time-delay, a novel delay-dependent stability result is derived. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones.

This paper is concerned with stability for aperiodic sampled-data systems. Firstly, for aperiodic sampled-data systems without uncertainties, a new Lyapunov-like functional is constructed by introducing the double integral of the derivative of the state, the integral of the state, and the integral of the cross term of the state and the sampled state. When estimating the derivative of the Lyapunov-like functional, superior integral inequalities to Jensen inequality are employed to get a tighter upper bound. By the Lyapunov-like functional principle, sampling-interval-dependent stability results are derived. Then, the stability results are extended to aperiodic sampled-data systems with polytopic uncertainties. Finally, some examples are listed to show the stability results have less conservatism than some existing ones.

This paper is concerned with robust stability for impulsive systems with polytope uncertainties. At first, the stability for impulsive systems without uncertainties is addressed by employing a Lyapunov-like functional. The Lyapunov-like functional is time-varying, discontinuous, and not imposed to be definite positive. Compared with the existing Lyapunov functional built on [t(k), t], a part of the impulsive interval [t(k), t(k+1)], the Lyapunov-like functional is two-sided in terms of employing the system information on [t, t(k+1)] as well as [t(k), t]. When estimating the derivative of the time-varying and two-sided Lyapunov-like functional, which includes integrals of the state and integrals coupled by [t, t(k+1)] and [t(k), t], integral equations of the impulsive system are introduced and an advanced inequality is employed. By the Lyapunov-like functional theory, a new stability result is obtained for impulsive systems without uncertainties. Then, the stability result is adapted to impulsive systems with polytopic uncertainties and a robust stability result is derived. At last, the numerical examples are given to illustrate that the stability results for impulse systems with or without polytopic uncertainties improve over some existing ones.

研究了变周期采样系统的采样区间依赖稳定性问题.采用类Lyapunov泛函方法研究采样系统的稳定性与采样区间的关系,该类Lyapunov泛函不强求正定也不要求连续.通过增加状态与状态导数的交叉项推广了类Lyapunov泛函,然后用新的不等式处理该类Lyapunov泛函的导数,基于类Lyapunov泛函方法导出了采样区间依赖稳定性新结果,然后,在凸多胞型不确定采样系统中推广该结果,得到了鲁棒采样渐近稳定性新准则.最后,用3个仿真例子说明了文章结果比现有的某些结果保守性小.

This study is concerned with the dwell-time stability for impulsive systems under periodic or aperiodic impulses. A Lyapunov-like functional approach is established to study the stability for impulsive systems. The Lyapunov-like functional is time-varying and decreasing but is not imposed definite positive nor continuous. A specific Lyapunov-like functional is constructed by introducing the integral of state together with the cross-terms of the integral and impulsive states. A tight bounding is obtained for the derivative of this functional with the help of the improved Jensen inequality reported recently and the integral equation of the impulsive system. On the basis of the Lyapunov-like functional approach, new dwell-time-dependent stability results with ranged dwell-time, maximal dwell-time and minimal dwell-time are derived for periodic or aperiodic impulsive systems. The stability results have less conservatism than some existing ones, which are illustrated by numerical examples.

A new Lyapunov functional is used to analyze the asymptotic stability of sampled-data systems under aperiodic sampling. A Lyapunov functional is constructed by introducing the integral of the state and the cross term of this integral and the sampling state. The improved Jensen inequality reported recently is used to estimate the derivative of the Lyapunov functional. A new asymptotic stability result is obtained for the sampled-data systems under aperiodic sampling. The simulation results show that the proposed result has less conservatism than some existing ones.

Summary This paper proposes a separation method of a transmission delay and data packet dropouts from a lumped input delay in the stability problem of a networked control system, where both the transmission delay and the data packet dropouts are involved. By modeling data packet dropouts as sampling processes and the transmission delay as a state delay, the networked control system is represented as a sampled‐data system with aperiodic sampling and a state delay. In order to separate the state delay and the sampling, the sampled‐data system is transformed into a new system with an integral operator, where the sampling is embedded into the integral operator. By investigating the integral operator's gain and passivity, a novel Lyapunov functional is constructed to address the stability problem. The obtained stability results are dependent on both the data packet dropouts and the time delay. A numerical example is provided to demonstrate that the stability results are less conservative than some existing ones. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with a Lyapunov-like functional approach to stability for impulsive systems with polytopic uncertainties. At first, a Lyapunov-like functional approach is established to investigate the stability for impulsive systems, with the Lyapunov-like functional dependent on time explicitly, discontinuous, and not imposed to be definite positive. A specific Lyapunov-like functional is created by introducing the integral of the system state and the cross terms among this integral and the impulsive state. To estimate the derivative of the functional, a new inequality is proposed, and an integral equation of the impulsive system is employed. By the Lyapunov-like functional theory, a new asymptotical stability result is obtained for impulsive systems without uncertainties. Then, the stability result is further extended to impulsive systems with polytopic uncertainties. At last, some numerical examples are given to illustrate that the proposed stability results have less conservatism than some existing ones.

In this paper, an adaptive tracking control scheme is presented for a class of nonlinear systems using nonlinearly parameterized first-order Sugeno fuzzy approximator. The parameters in the first-order Sugeno consequents and Gaussian basis functions are assumed to be unknown. First, based on the parameterization of the exponential function, a new parameterization model of first-order Sugeno fuzzy system is developed. The new representation of unknown system function is constructed by exploiting the signal replace approach. Then, unknown fuzzy parameters and known functions with the tracking elements being arguments are collected, respectively, and some new parameters and useful functions are defined, respectively. Furthermore, adaptive controller is designed and analyzed. Global boundedness of the closed-loop system is established, and asymptotic tracking is achieved. Finally, the simulation results demonstrate the effectiveness of the proposed scheme.