Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays.

Exponential Stability of Large-Scale Non-Linear Systems with Multiple The Delays

The problem of stabilizing a class of large-scale non-linear multiple delay systems is considered.The complicated system is decomposed into several subsystems; each function of them is expressed by a set of components of the overall state vector,with interconnections between them, and the subsystems are coupled by the delayed state. In this paper, a method is devised to be a suitable choice of state feedback controls of every subsystems, moreover, it is proved that the large-scale system is exponential stable.

Partial stability of a class of large-scale systems with partiallystable isolated subsystems

The problem of partial stability is investigated for a class of continuous-time large-scale systems. Under assumption that the null solution of the isolated subsystems is stable, based on decomposition-aggregation methods and Lyapunov second method, some theorems concerning the globally partial asymptotic stability and globally partial exponential stability are obtained via utilizing the inequality analysis technique and comparison technique. Finally, an example is presented to illustrate the results.

THE ASYMPTOTIC STABILITY OF THE LINEAR.DISCRETE LARGE-SCALE SYSTEMS

In this paper, we directly use the tirear norm Liapunov function to investigate the stability of the linear discrete large-scale systems and obtain some criteria for the asymptotic stability of such a system.

A New Criterion for Stability of Large-Scale Systems with Delay

A simple criterion for delay-independent stability of large-scale linear time-varying systems is deduced by employing a type of Lyapunov function. The notable features of the results in this paper are its simplicity and efficiency in testing the stability large-scale linear time-varying systems. Some illustrative examples are given to demonstrate the advantages of the obtained results over those in literature.

On the conjunction practical stability and controllability of large-scale impulsive control systems

We studied the conjunction practical stability and controllability of large-scale impulsive control systems by using the comparison systems and vector Lyapunov fimctions. Then the less conservative sufficient conditions for conjunction practical stability and controllability of large-scale impulsive control system were obtained.

Sufficient Conditions for Robust Stability of Discrete Large-Scale Interval Systems with Multiple Time Delays

The robust stability analysis for discrete large-scale uncertain systems with multiple time delays is addressed in this paper. We establish a method for selecting properly a positive definite matrix Q to derive a very simple upper solution bound of the discrete algebraic Lyapunov equation (DALE). Then, using the Lyapunov equation approach method with this upper bound, several sufficient conditions are presented to guarantee the robust stability of the overall systems. Comparisons between the proposed results with a previous one are also given.

STABILITY OF NONLINEAR COMPARISON EQUATIONS FOR DISCRETE LARGE-SCALE SYSTEMS

On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C, is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.

Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems

This paper studies deterministic and stochastic fixedtime stability of autonomous nonlinear discrete-time(DT)systems.Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified.Extensions to systems under deterministic perturbations as well as stochastic noise are then considered.For the former,sensitivity to perturbations for fixed-time stable DT systems is analyzed,and it is shown that fixed-time attractiveness results from the presented Lyapunov conditions.For the latter,sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented.The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems,and a stochastic settling-time function fixed upper bound is derived for stochastic DT systems.Illustrative examples are given along with simulation results to verify the introduced results.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Intelligent Smart Grid Stability Predictive Model for Cyber-Physical Energy Systems

A cyber physical energy system(CPES)involves a combination of pro-cessing,network,and physical processes.The smart grid plays a vital role in the CPES model where information technology(IT)can be related to the physical system.At the same time,the machine learning(ML)modelsfind useful for the smart grids integrated into the CPES for effective decision making.Also,the smart grids using ML and deep learning(DL)models are anticipated to lessen the requirement of placing many power plants for electricity utilization.In this aspect,this study designs optimal multi-head attention based bidirectional long short term memory(OMHA-MBLSTM)technique for smart grid stability predic-tion in CPES.The proposed OMHA-MBLSTM technique involves three subpro-cesses such as pre-processing,prediction,and hyperparameter optimization.The OMHA-MBLSTM technique employs min-max normalization as a pre-proces-sing step.Besides,the MBLSTM model is applied for the prediction of stability level of the smart grids in CPES.At the same time,the moth swarm algorithm(MHA)is utilized for optimally modifying the hyperparameters involved in the MBLSTM model.To ensure the enhanced outcomes of the OMHA-MBLSTM technique,a series of simulations were carried out and the results are inspected under several aspects.The experimental results pointed out the better outcomes of the OMHA-MBLSTM technique over the recent models.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

Preliminary Study on the Effect of Different Ecological Cultivation Modes on the Water Stability of Soil Aggregates in Rubber Based Agroforestry Systems

Rubber trees (Hevea brasiliensis Müll. Arg.) have been commercially cultivated for a century and a half in Asia, particularly in China, and they constitute a common element of plantation ecosystems in tropical regions. Soil health is fundamental to the sustainable development of rubber plantations. The objective of the study is to explore the influence of different complex ecological cultivation modes on the stability of soil aggregates in rubber based agroforestry systems. In this study, the ecological cultivation mode of rubber—Alpinia oxyphylla plantation, the ecological cultivation mode of rubber—Phrynium hainanense plantations, the ecological cultivation mode of rubber—Homalium ceylanicum plantations and monoculture rubber plantations were selected, and the particle size distribution of soil aggregates and their water stability characteristics were analyzed. The soil depth of 0 - 20 cm and 20 - 40 cm was collected for four cultivation modes. Soil was divided into 6 particle levels > 20 cm. soil was divided into 6 particle levels > 5 mm, 2 - 5 mm, 1 - 2 mm, 0.5 - 1 mm, 0.25 - 0.5 mm, and 0.053 - 0.25 mm according to the wet sieve method. The particle size proportion and water stability of soil aggregates were determined by the wet sieve method. The particle size proportion and water stability of soil aggregates under different ecological cultivation modes were analyzed. The results showed that under different ecological cultivation modes in the shallow soil layer (0 - 20 cm), the rubber—Alpinia oxyphylla plantation and the rubber—Phrynium hainanense plantation promoted the development of dominant soil aggregates towards larger size classes, whereas the situation is the opposite for rubber—Homalium ceylanicum plantation. In soil layer (20 - 40 cm), the ecological cultivation mode of rubber—Phrynium hainanense plantation developed the dominant radial level of soil aggregates to the diameter level of large aggregates. Rubber—Alpinia oxyphylla plantation and rubber—Homalium ceylanicum plantation, three indicators, including the water-stable aggregate content R0.25 (>0.25 mm water-stable aggregates), mean weight diameter (MWD), and geometric mean diameter (GMD), were all lower than those in the rubber monoculture mode. However, in the rubber—Phrynium hainanense plantation, the water-stable aggregate content R0.25, mean weight diameter, and geometric mean diameter were higher than in the rubber monoculture mode, although these differences did not reach statistical significance.

Guaranteed Quadratic Stabilization of Certain Time-Varying Large-Scale Delay It Stochastic Systems

In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.

DECENTRALIZED STABILIZATION OF LARGE-SCALE LINEAR INTERCONNECTED SYSTEMS WITH TIME-VARYING DELAYS

The decentralized stabilization conditions for large-scale linear interconnection systems with time-varying delays were established by using some different decomposition cases of interconnection matrices, and a method for designing the decentralized local memoryless state feedback controllers was proposed. All of the considered delays are continuous function, and satisfy some conditions.

Stability Analysis of Continuous-Time Fuzzy Large-Scale System

A continuous-time fuzzy large-scale system F consists of some interconnected Takagi-Sugeno fuzzy subsystems. Two sufficient conditions for the asymptotic stability of this system (namely, theorem 1 and theorem 2) are derived via a multiple Lyapunov function approach. In theorem 1, the information of membership functions of fuzzy rules should be known in order to analyze the stability of F. But in general this information is not easy to be acquired for their time-varying property. So theorem 2 is provided to judge the asymptotic stability of F, based on which there is no need to know the information of membership functions in stability analysis. Finally, a numerical example is given to show the utility of the method proposed in this paper.

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

Fixed-Time Antidisturbance Consensus Tracking for Nonlinear Multiagent Systems With Matching and Mismatching Disturbances

In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.

A PID Tuning Approach for Inertial Systems Performance Optimization

In the practice of control the industrial processes, proportional-integral-derivative controller remains pivotal due to its simple structure and system performance-oriented tuning process. In this paper are presented two approaches for synthesis the proportional-integral-derivative controller to the models of objects with inertia, that offer the procedure of system performance optimization based on maximum stability degree criterion. The proposed algorithms of system performance optimization were elaborated for model of objects with inertia second and third order and offer simple analytical expressions for tuning the PID controller. Validation and verification are conducted through computer simulations using MATLAB, demonstrating successful performance optimization and showcasing the effectiveness PID controllers’ tuning. The proposed approaches contribute insights to the field of control, offering a pathway for optimizing the performance of second and third-order inertial systems through robust controller synthesis.

Stability of Difference Systems with Finite Delay

In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.