Stabilization Problem Of Systems Research Articles

Dynamic quantization‐driven stability of networked control systems under DoS attacks

AbstractThis paper focuses on the stability problem of networked control systems (NCSs) under denial‐of‐service (DoS) attacks and bandwidth limitation. Firstly, the periodic dynamic quantization mechanism is extended to insecure systems, and a periodic‐like quantization strategy is proposed. Due to the designable period, such mechanism allows a trade‐off between better system performance and less energy consumption. With finite quantization levels, a reasonable parametric design is given to avoid quantizer saturation under general energy‐constrained DoS attacks. Secondly, a suitable quantized controller is designed for the system affected by DoS attacks. The relationship between the quantized controller and the DoS attacks is analyzed, and the criterion for NCSs achieving global asymptotic stability is derived. Finally, two numerical examples are given to verify the correctness of the theoretical result.

A Comprehensive Review on the Modelling and Significance of Stability Indices in Power System Instability Problems

Many technological advancements in the modern era have made actual use of electrical power and the constrained operating of power systems within stability limits. Some expeditious load variations and rising power demands initiate complications in voltage stability and can put stress on performance, leading to voltage instability. Voltage Stability Indices can be used to perform voltage stability assessment. This review evaluates various VSIs based on mathematical derivations, assumptions, critical values, and methodology. VSIs determine the maximum loadability, voltage collapse proximity, stability margin, weak areas, and contingency ranking. Stability indices can also specify the optimal placing and sizing of Distributed Generators. Thus, VSIs play a vital role in power system voltage stability. This review is a comprehensive survey of various indices and analyses their accuracy in determining the instability of power systems. Voltage stability is a crucial concern in operating a reliable power system, and the systematic evaluation of voltage stability is essential in a power system. This review considered and analyzed 34 indices from 138 articles from the literature for their significant performance in various power system stability problems. Of 33 indices, were 22 derived from transmission line parameters, referred to as line indices, and 12 from bus and line parameters, referred to as bus indices.

The stabilization of uncertain dynamic systems involving the generalized Riemann-Liouville fractional derivative via linear state feedback control

The main objective of this paper is to investigate the stabilization problem of uncertain fractional-order dynamic systems (UFDSs) that involve the generalized Riemann-Liouville fractional derivative using a linear feedback controller. We establish several sufficient conditions for achieving Mittag-Leffler stabilization and asymptotic stabilization of UFDSs. The primary methodology employed in our study is Lyapunov's direct method (LDM), along with other inequality techniques, which have demonstrated significant efficacy in studying the stability theory of nonlinear dynamic systems. To demonstrate the effectiveness of the proposed approach, examples and corresponding simulations are provided.

Event-triggered distributed delayed impulsive control for nonlinear systems with applications to complex networks

This paper studies the Lyapunov stability of general nonlinear systems and the synchronization of complex networks via event-triggered impulsive control (ETIC), where the distributed delayed impulses are fully considered. Some sufficient conditions are given to deal with the problem of Lyapunov stability for nonlinear systems and avoid Zeno behavior based on distributed delayed ETIC. Moreover, some relationships between the distributed delays in impulses, the triggering parameters, and the impulsive parameters are constructed. Then, as an application, we apply the above theoretical results to complex networks and design a kind of distributed delayed ETIC strategy to ensure synchronization of complex networks under distributed delayed ETIC. In the end, the validity of our proposed results is proved by two numerical examples.

Leader–follower sliding mode formation control of fractional-order multi-agent systems: A dynamic event-triggered mechanism

This paper examines the concept of the leader–follower formation for fractional-order multi-agent systems (FO-MASs) by utilizing dynamic event-triggered sliding mode control (SMC) method. Firstly, a dynamic event-triggered mechanism (DETM) is designed relying on the combined measurement vector, in which an auxiliary variable is introduced to dynamically adjust the threshold for each fractional-order agent system. Unlike most existing event-triggered communication mechanisms, whose threshold parameters are always fixed, the threshold parameters in our designed event-triggered conditions can be dynamically adjusted according to the fractional-order dynamic rule. Numerical results show that the proposed DETM can achieve a better system performance in reducing the sampling frequency and the expected formation performance. Secondly, the leader–follower formation control problem is transformed into checking the asymptotic stability problem of the closed-loop system. In addition, due to the memorability of fractional calculus operators, a distinctive condition is established to avoid the occurrence of Zeno behaviors reported in existing dynamic event-triggered schemes. Finally, a simulation example is presented to illustrate the effectiveness and feasibility of the dynamic event-triggered SMC method proposed in this paper.

Exponential stability of nonlinear systems via event-triggered impulsive control based on partial states

In the framework of partial unknown states, this paper studies the exponential stability problem of nonlinear systems. A novel event-triggered mechanism (ETM) just involving partial known states is designed to guarantee the exponential stability of considered system, where forced impulse with great freedom degree is introduced in ETM. What's more, the information of known states of the system is fetched and applied to supplement the unknown part at impulse instants. With the help of matrix analysis technique, some linear matrix inequalities (LMI) based sufficient conditions are presented from the perspective of the quantity of known and unknown states. Besides, our proposed conditions establish the relationship of event-triggered parameters, impulse interval, and impulse strength. Finally, expository examples and their numerical modeling are appeared to prove the availability of main results.

Robust tracking control for uncertain fuzzy systems with time delay and external disturbances

AbstractIn this article, robust tracking and disturbance rejection problem for Takagi–Sugeno fuzzy systems with time delay and external disturbances are discussed. Specifically, proportional‐integral controller with an enhanced equivalent‐input‐disturbance technique is constructed to force the output trajectories to track the bounded reference input signal even in the presence of external disturbances. Further, the resulting fuzzy control system can be represented as an augmented system with state delay and uncertainties and the output tracking problem is transformed into stabilization problem of the augmented system. In the stabilization analysis, the considered fuzzy system does not share the same membership functions with the proposed control. Moreover, the delay‐dependent stabilization criteria for the addressed fuzzy system are presented in the form of linear matrix inequalities by the virtue of augmented Lyapunov–Krasovskii functional. To be specific, the symmetric matrices involved in the Lyapunov–Krasovskii functional need not be positive definite. Ultimately, three numerical examples are offered to support the validity of the established theoretical results.

Simulation of Secondary Frequency Modulation Process of Wind Power with Auxiliary of Flywheel Energy Storage

With the rapid increase in the proportion of wind power, the frequency stability problem of power system is becoming increasingly serious. Based on MATLAB/Simulink simulation, the role and effect of secondary frequency modulation assisted by Flywheel Energy Storage System (FESS) in regional power grid with certain wind power penetration rates are studied. First, the linear frequency control of the power system is used to establish the primary frequency modulation control model of FESS assisting wind power, and the frequency characteristics of FESS participating in primary frequency modulation are analyzed according to the transfer function. Then, in the case of step disturbance and continuous disturbance of load power, the frequency characteristics of a regional power grid are simulated and demonstrated through time domain simulation, and conclusions are drawn through comparison; a certain proportion of FESS can quickly respond to the frequency deviation signal. During secondary frequency modulation simulation, the maximum frequency deviation of the system is reduced by 57.1% and the frequency fluctuation range is reduced by 53.8%, effectively improving the frequency quality of the power grid.

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

This paper addresses the fixed-time stability problem of chaotic systems with internal uncertainties and external disturbances. To this end, new sliding-mode surfaces are introduced to design fixed-time controllers for the stabilization of perturbed chaotic systems. First, the required conditions for deriving fixed-time stability are determined. Then, using the obtained stability theorems and sliding mode techniques, the controllers are synthesized. The proposed controller enables the convergence of the trajectories of the chaotic system to the origin in finite time, independently of the initial conditions. The performance of the proposed approach is assessed using a simulation study of a PMSM system and the Matouk system. Among the advantages of the proposed controller are its robustness to external disturbances and the boundedness of the settling time to a constant value for any initial condition.

A Sufficient Condition on Polynomial Inequalities and its Application to Interval Time-Varying Delay Systems

This article examines the stability problem of systems with interval time-varying delays. In the derivation of Lyapunov–Krasovskii functional (LKF), non-convex higher-degree polynomials may arise with respect to interval time-varying delays, making it difficult to determine the negative definiteness of LKF’s derivative. This study was conducted to obtain stability conditions that can be described as linear matrix inequalities (LMIs). By considering the idea of matrix transition and introducing the delay-dependent augmented vector, a novel higher-degree polynomial inequality is proposed under the condition that the lower bound of the polynomial function variable is non-zero, which encompasses the existing lemmas as its special cases. Then, benefiting from this inequality, a stability criterion is derived in terms of LMIs. Finally, several typical examples are presented to verify the availability and strength of the stability condition.

STABILIZATION OF DISCRETE-TIME SYSTEMS WITH STATE-DELAYS AND SATURATING CONTROL INPUTS

Context. The presence of time delays occurs in many complex dynamical systems, particularly in the areas of modern communication and information technologies, such as the problem of stabilizing networked control systems and high-speed communication networks. In many cases, time-delays lead to a decrease in the efficiency of such systems and even to the loss of stability. In the last decade, many interesting solutions using the Lyapunov-Krasovskii functional have been proposed for stability analysis and synthesis of a stabilizing regulator for discrete-time dynamic systems with unknown but bounded state-delays. The presence of nonlinear constraints on the amplitude of controls such as saturation further complicates this problem and requires the development of new approaches and methods.
 Objective. The purpose of this study is to develop a procedure for calculating the control gain matrix of state feedback that ensures the asymptotic stability of the analyzed system, as well as a procedure for calculating the maximum permissible value of the state-delay under which the stability of the closed-loop system can be ensured for a given set of admissible initial conditions.
 Method. The paper uses the method of descriptor transformation of the model of a closed-loop system and extends the invariant ellipsoids method to systems with unknown but bounded state-delays. The application of the Lyapunov-Krasovskii functional and the technique of linear matrix inequalities made it possible to reduce the problem of calculating the control gain matrix to the problem of semi-definite programming, which can be solved numerically. An iterative algorithm for solving the bilinear matrix inequality is proposed for calculating the maximum permissible value of the time-delay.
 Results. The results of numerical modeling confirm the effectiveness of the proposed approach in the problems of stabilizing discrete-time systems under the conditions of state-delays and nonlinear constraints on controls, which allows to recommend the proposed method for practical use for the problem of stability analysis and synthesis of stabilizing regulator, as well as for calculating the maximum permissible value of time-delay.
 Conclusions. An approach is proposed that allows extending the invariant ellipsoids method to discrete-time dynamic systems with unknown but bounded state-delays for solving the problem of system stabilization using static state feedback based on the application of the Lyapunov-Krasovskii functional. The results of numerical modeling confirm the effectiveness of the proposed approach in the presence of the saturation type nonlinear constraints on the control signals.

Lyapunov functionals for linear continuous-time difference systems: A single delay case

This paper focuses on the Lyapunov stability problem of linear continuous-time difference systems. We show that although the stability of these systems has been extensively investigated, the problem of determining suitable quadratic Lyapunov functionals is not completely solved yet, even for the simplest system with a single delay. Herein, using the single delay case as an example, we construct new quadratic Lyapunov functionals. The functionals, which depend on a matrix-valued function strongly related to the discrete-time Lyapunov matrix equation, allow deriving a converse Lyapunov functional result. We show how the functionals can be used to solve problems such as the computation of exponential estimates for solutions and robustness bounds of perturbed systems.

Novel Stability and Stabilization Conditions of Linear Fractional-Order Time-Delay Systems Using Free Matrix Approach

The stability and stabilization problem of linear fractional-order time-delay systems is investigated. By introducing a free matrix, the linear fractional-order time-delay systems is transformed to a delay-free system interconnected with uncertainties. New stability and stabilization criteria are derived based on the small gain theorem. The criteria are formulated as linear matrix inequalities and are computationally efficient. Since the free matrix is utilized, the new conditions are less conservative than the existing ones. Two numerical examples indicate that the proposed criteria are less conservative than existing ones.

Data-Driven Security and Stability Rule in High Renewable Penetrated Power System Operation

Power systems around the world are experiencing an energy revolution that substitutes fossil fuels with renewable energy. Such a transition poses two significant challenges: highly variable generators that add short-term and long-term difficulties for supply–demand balance, and a high proportion of convertor-based devices that may jeopardize power system security and stability. At the same time, machine learning techniques provide more opportunities to study the complex power system security and stability problems. This article summarizes the machine learning framework to embed security rules into power system operation optimization under high renewable energy penetration. First, we explore how high penetration renewable energy impacts power system security and stability. Then, we review how the complex security and stability boundary of power systems is modeled using various machine learning techniques. Finally, we show how the machine learning model is transformed into optimization constraints that can be embedded into the power system operation model. The framework is substantiated through case studies of practical power systems.

Global Finite-Time Stabilization of First-Order Systems With Bounded Controls

This paper addresses the global finite-time stabilization problem for systems with bounded controls. First, based on the bounded functions of tanh(∙) and arctan(∙), two classes of bounded global finite-time controllers are proposed to stabilize single integrator systems and the saturation level of the control input can be prescribed. In addition, for each proposed controller, the upper-bound estimate for closed-loop settling time is provided explicitly, which is closely related to a parameter reflecting the initial state location. Finally, the effectiveness of the proposed controllers is verified through simulation.

HVDC 운영 전략에 따른 제주 전력 계통의 출력제어 및 운영비용 분석

The proportion of renewable power generation in power systems is rapidly increasing, resulting in frequent imbalances. This paper focuses on the impact of renewable energy penetration on power system stability in Jeju, South Korea, under the CFI 2030 policy. With the increase in renewable energy sources, power variability has also increased due to their intermittent nature, leading to supply and demand imbalances and system stability problems. Traditional methods of maintaining power balance, such as curtailment, result in cost and environmental losses for system operators. To address this issue, the paper proposes the use of HVDC power reversal transmission strategies to return excess power from Jeju to the mainland power system. The study analyzes the impact of three operational strategies of HVDC on unit commitment results, considering cost and environmental factors. The results suggest that using HVDC can mitigate curtailment and reduce oversupply, leading to improved power system stability in Jeju island.

Stabilization of Discrete-Time Systems with Random Delays and Packet Drops: A Predictor-Like Controller

In this paper, we study stabilization of discrete-time systems in which control inputs are transmitted over a random delay and packet drop channel. A predictor-like linear feedback controller is proposed by a reduction technique in which the reduced system has the same dimension as that of the original system. A necessary and sufficient condition to stabilize the original system in the mean-square sense is obtained based on an algebraic Riccati equation. Some necessary and sufficient stabilizability conditions based on the Lyapunov criterion are also presented. Interestingly, it is shown that the stabilization problem considered in this paper is equivalent to the stabilization problem of a particular delay-free system with control-dependent correlated noises. Simulation examples are provided to illustrate the effectiveness and advantages of the proposed stabilizing controller.

Optimal Control of Technological Processes

The paper formulates conditions under which the roots closest to the imaginary axis (critical roots) of the characteristic equation of a linearized system are real for the maximum possible degree of stability of the closed-loop control system of a technological process with pure delay. For the parameters of the controllers corresponding to the maximum degree of stability, these roots are multiples. Their multiplicity order is one more than the number of coefficients in the transfer function of the controller. It is demonstrated that for a typical technological control object, these conditions are satisfied for all “serial” control laws. This allowed for obtaining analytical expressions for optimal settings and limiting degrees of stability as functions of object parameters for typical dynamic characteristics of technological processes. The paper considers the problem of robust stability for control systems with an object containing pure delay. It has been proven that in the maximum stability problem, the operations of maximizing over controller parameters and minimizing over the set of possible object parameters can be interchanged. Therefore, selecting robust settings amounts to determining the minimum of the maximum stability over the set of possible object parameter values. Controllers with such settings are suitable, without modification, for a whole class of technological processes.

Analisis Kestabilan Transien Akibat Penambahan Generator di Pabrik Gula

The Assembagoes sugar factory has a production capacity of 3000 TCD and was revitalized in 2015, increasing the capacity to 6000 TCD. With the increase in production capacity, the supply of electrical energy, which had previously only come from one generator unit, was supplemented with one new 13 MW generator unit, increasing the total generation capacity to 23 MW. With this addition, the operation pattern of the electrical system changes, and the problem of system stability becomes one of the primary concerns that must be analyzed with improvements to the Assembaggoes sugar factory's electrical system. The goal of this research is to determine the system's frequency and voltage response when a brief stability disturbance occurs.

Voltage and frequency instability in large PV systems connected to weak power grid

The voltage and frequency control of photovoltaic (PV) systems are influenced by coupled nonlinear factors. It has been discovered that frequency control stability is threatened by voltage regulation methods in PV systems. However, the frequency instability caused by voltage regulation methods has not been fully investigated. This paper investigates the voltage and frequency stability problems in PV systems connected with weak power grids. The voltage problems caused by grid impedance, comprising inverter AC voltage and DC voltage, are first analyzed. Then, methods for improving voltage stability, such as reactive power compensation, and the benefits and drawbacks of various compensation methods are investigated. Finally, the effect of reactive power compensation on frequency control stability is investigated and resolved. Simulations and experiments are used to validate the theory’s correctness.