Delay-dependent Stability Research Articles

Load frequency control of time-delayed power system based on event-triggered communication scheme

In frequency regulation of power grids, conveying observations to controllers and obtaining control outputs depend greatly on communication and computation resources. Particularly for modern power system with an open communication network, the costs of communication and computation should not be ignored. This paper investigates an event-triggered based load frequency control for time-delayed power system with an open communication network. Based on the lifting technique in the sampled-data control theory, a new control scheme, using both a large sampling period and a maximized threshold parameter, is introduced to further lessen communication and computation costs while preserving a desired H∞ robust performance. The delay-dependent stability criterion of the proposed control scheme is less conservative, which takes fully the time delay, the sampling period, and the threshold parameter of event-triggered communication scheme into account. The proposed criterion is unified and can be transformed to the stability conditions of the existing research by setting different values of time delay, sampling and threshold parameter. Additionally, the usage of a large and aperiodic sampling period complies with the aperiodic updating characteristic of 2-4s in control signals in load frequency control scheme. Case studies based on a one-area power system, a two-area power system and an IEEE 39-bus benchmark test system are carried out. The simulation tests demonstrate that the proposed control scheme further reduces the communication and computation costs and ensures the load frequency control system stable operation with a preset H∞ robust performance.

Determination of stability delay margins for multi-area load frequency control systems with incommensurate time delays through eigenvalue tracing method

This work presents delay-dependent stability analysis using eigenvalue tracing method for multi-area load frequency control (LFC) systems with incommensurate time delays. LFC systems face inevitable communication delays that adversely affect the frequency stability. Time delays exceeding the allowable limit lead to system instabilities. In this study, stability delay margins of a time-delayed LFC system are computed by a simple yet effective frequency-domain method for computing critical eigenvalues and the corresponding delay margins without using the characteristic equation of the system. By tracing eigenvalue loci of a transformation matrix, the method easily determines the critical eigenvalues on the imaginary axis and obtains stability delay margins. Both stability delay margins and the effectiveness of stability regions in the time delay space are confirmed by time-domain simulations and the quasi-polynomial mapping-based root finder (QPmR) algorithm. Results indicate that more accurate delay margin values are obtained as compared to ones with Lyapunov stability theory based algorithms.

Takagi–Sugeno State Delayed Feedback and Integral Control for PV Systems: Modeling, Simulation, and Control

The integration of the large-scale photovoltaic systems has experienced significant growth, which is similarly expected to occur with small-scale photovoltaic systems. Since small-scale systems must be simple in cost-effective components, control strategies must be implemented in low complexity circuits. However, current maximum power point tracking (MPPT) algorithms are generally complex and require electronic components to support variable control gains for different irradiance conditions, preventing simple MPPT implementations suitable for small-scale photovoltaic systems. This paper proposes a new control strategy to tackle the power tracking problem of the power systems. First, a dynamic model of the photovoltaic system is described and converted into a Takagi–Sugeno (T-S) model. Then, an MPPT scheme is proposed in series with a fixed integral and a fuzzy gain state delay feedback controller, which avoids the need for a variable control gain, simplifying the electronic implementation of the control strategy. New delay-dependent stabilization conditions based on the Lyapunov-Krasovskii functional are proposed in terms of a convex optimization problem, where the delayed feedback and integral gains are designed simultaneously. Simulation results using Matlab and Simulink are used to validate the proposed method.

Robust stabilization of T-S fuzzy systems via improved integral inequality

This paper addressed the robust stabilization performance of Takagi–Sugeno (T-S) fuzzy systems under a state feedback controller. To attain this, an integral inequality is proposed by rearranging the quadratic matrix-vector form combined with Jensen’s inequality to handle the single integral terms obtained by taking the derivative of the concerned Lyapunov–Krasovskii functional. By employing this integral inequality and by using integral inequality techniques, some improved delay-dependent stability and stabilization results are established in terms of linear matrix inequalities for the proposed T-S fuzzy model. Finally, some numerical examples are provided to facilitate the feasibility and less conservativeness of the proposed theoretical results.

Non-fragile state estimation for memristive cellular neural networks with proportional delay

This paper focuses on modeling a non-fragile state estimator for a class of memristive cellular neural networks (MCNNs) with proportional delay. Due to the state transition characteristics of memristor, the parameters of MCNNs are state-dependent. A discontinuous robust control scheme is applied to address such parameters issue. Using this control scheme, we have derived sufficient conditions to ensure the existence of a non-fragile state estimator for the supposed system. Through the Lyapunov stability analysis and matrix-based inequality techniques, delay-dependent stability criteria are obtained in the form of linear matrix inequalities (LMIs), which shows the asymptotic stableness of the prescribed error system under the consideration of all possible gain variations. Besides, the control gain components are obtained by solving the resulting LMIs using some available MATLAB algorithms. Lastly, to facilitate the efficacy of the proposed estimator design, numerical simulations are examined.

Investigation on stability of delayed T-S fuzzy interconnected systems via decentralized memory-based sampled-data control and validation through interconnected power systems with DFIG-based wind turbines

This study investigates the stability of nonlinear interconnected systems (ISs) with time-delays by designing a decentralized memory-based sampled-data control and it’s an application to power system with doubly fed induction generator (DFIG)-based wind turbines (WTs). Initially, a nonlinear delayed IS is expressed as a delayed Takagi-Sugeno fuzzy ISs based on fuzzy IF-THEN membership rules. Following that, a decentralized sampled-data controller with a memory parameter is designed to ensure the stabilization of the considered ISs. Through constructing Lyapunov-Krasovskii functional by involving the information about the time-delays and sampling periods, delay-dependent stability and stabilization conditions are derived in terms of linear matrix inequalities. The sufficient conditions are guaranteed the asymptotic stability of the closed-loop ISs under a prescribed level of H∞ performance via a decentralized controller. To validate the derived theoretical sufficient conditions, a nonlinear interconnected power systems with DFIG-based WTs is modeled in which a time-delay is considered in the area control error (ACE). Finally, simulation results of the two area ISs are provided to illustrate the effectiveness of the derived theoretical conditions under the designed controller.

Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

Time delay margins computation for stability of load frequency control in hybrid renewable energy power generation/storage system

In load frequency control (LFC), it is important to transmit control signals from remote terminal units (RTU) to the control center and from the control center to the plant side. Therefore, time delays in signal transmission become unavoidable. These delays reduce the dynamic performance of the LFC system. This paper is dedicated to the delay-dependent stability analysis of the LFC scheme for renewable energy power generation subsystem. The delay margin of the system is analyzed theoretically for different values of inertia, damping factor as well as controller gains. Theoretically obtained results are compared with simulation studies. The relation between the controller gain and the delay margin is investigated. The system studied includes photovoltaic system (PV), ultra-capacitor (UC) bank for energy storage, wind turbine generator (WTG), diesel generator (DG) and fuel cell (FC) system. The upper bound of the delay time, while LFC system is in stable condition, is known as delay margin. Delay margin computations are realized by using an analytical method approach. Proportional-integral (PI) controller is used for controlling proposed power generation storage system. PI Controller parameters are chosen in a wide range to observe the effect of the parameter space on delay margin variation. Simulation studies verify the effectiveness of the proposed method.

Stabilisation for 2-D discrete-time switched nonlinear systems with mixed time-varying delays under all modes unstable

The problem of delay-dependent stability is concerned for two-dimensional switched systems in Fornasini-Marchesini local state-space model with mixed time-varying delays and with a class of generalised Lipschitz nonlinearities in this paper. The mixed time-varying delays consist of both the discrete and the distributed delays, and the time-varying delays are allowed in the states. Adopting the fast average dwell-time switching technique with Lyapunov functional, a sufficient condition of the exponential stability for two-dimensional nonlinear switched systems with all subsystems unstable is derived in terms of linear matrix inequality. Specifically, two-dimensional Abel lemma-based finite-sum inequalities approach and Jensen inequalities approach are applied to reduce the conservativeness of the result. The obtained result on stability analysis is then utilised to design a dynamic output feedback controller to stabilise the nonlinear closed-loop switched system. Finally, two numerical examples are shown to demonstrate the validity of the proposed results.

Stochastic stabilization of Markovian jump neutral systems with fractional Brownian motion and quantized controller

This paper explores the delay dependent stochastic stabilization of Markovian jump neutral systems (MJNS) which are modeled by fractional Brownian motion(fBm) via a quantized controller. A function Round quantizer is introduced which solves the model uncertainties and the nonlinear part by a uniform operator. Then by structuring a Lyapunov–Krasovskii functional (LKF) and the aid of linear matrix inequalities (LMIs) method, a stochastic stability criterion is achieved. Last, different parameters are selected to simulate the effectiveness of our findings.

Observer-Based Stabilization of Linear Discrete Time-VaryingDelay Systems

Abstract This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov–Krasovskii (LK) functional to derive delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus ensure global asymptotic stability in presence of any time-delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

A novel integral inequality and its application to stability analysis of linear system with multiple time delays

The integral inequality plays a key role in developing delay-dependent stability criteria for the linear system with multiple time delays. This paper investigates a novel integral inequality to bound the integral terms in the derivative of the Lyapunov–Krasovskii functional (LKF). Compared with the auxiliary function-based integral inequality, the presented integral inequality is more general. By removing the involved auxiliary function, the integral term in the bound is linearly represented with a sequence of integrals only related to the system state. After a newly augmented LKF is constructed with multiple integral terms concerning the relationships among multiple delays, an adjustable and relaxed stability criterion is established in terms of linear matrix inequalities using the proposed inequality. Two numerical examples are given to show the merits of the proposed method.

Delay-Dependent Stabilization of Time-Delay Systems with Nonlinear Perturbations

Delay-Dependent Stabilization of Time-Delay Systems with Nonlinear Perturbations

Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation

Abstract In this article, we address the delay-dependent robust stability of uncertain fractional order neutral-type (FONT) systems with distributed delays, nonlinear perturbations, and input saturation. With the aid of the Lyapunov–Krasovskii functional, criteria on asymptotic robust stability of FONT, expressed in terms of linear matrix inequalities, are constructed to compute the state-feedback controller gains. The controller gains are determined subject to maximizing the domain of attraction via the cone complementarity linearization algorithm. The theoretical results are validated using numerical simulations.

Novel Delay-Dependent Stabilization for Fuzzy Stochastic Systems with Multiplicative Noise Subject to Passivity Constraint

A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.

New Criterion of Robust Hܣ Stabilization for Uncertain Neutral Systems

The problems of delay-dependent robust stability and stabilization for a class of uncertain neutral systems are investigated in this paper. At first, by constructing a new Lyapunov functional and using the Lyapunov stability theory, a new delay-dependent condition which renders the system with no external disturbance and input to be asymptotically stable is obtained and given by a linear matrix inequality. Then, based on the obtained condition, a state feedback stabilize law is designed, which guarantees closed-loop neutral systems are asymptotically stable for all the permitted uncertainties when the external disturbance is naught, and it can also guarantee the closed-loop systems have performance under the external disturbance. The model of neutral systems with both the uncertainty and the disturbance discussed in this paper has rarely been considered before.

An explicit robust stability condition for uncertain time-varying first-order plus dead-time systems

First-order plus dead-time (FOPDT) models are broadly used in process control to represent damped dynamic processes with time delays. An explicit condition for parameter- and delay-dependent robust stability of FOPDT systems with varying uncertain parameters and delay is derived in this paper. An internal model control (IMC) approach is proposed to parameterize stabilizing controllers that satisfy the output tracking objective in time-varying FOPDT systems represented by an uncertain first-order dynamic model with a time-varying delay in the control input. The small-gain theorem is used to derive an explicit necessary and sufficient parameter-dependent robust stability condition as a function of the nominal system gain, nominal varying delay, nominal time constant, and the bounds of the parameter uncertainties. An equivalent proportional-integral-derivative (PID) controller is then extracted to facilitate the implementation of the proposed IMC-based robust control. The application of the proposed explicit robust stability condition is studied in the context of air-fuel ratio (AFR) control in lean-burn spark ignition (SI) engines with a large time-varying transport delay in the control loop due to the placement of the universal exhaust gas oxygen (UEGO) sensor downstream the catalytic converter.

Delay-dependent stability analysis of nonlinear truck-trailer systems based on non-fragile memory sampled-data via fuzzy control

Delay-dependent stability analysis of nonlinear truck-trailer systems based on non-fragile memory sampled-data via fuzzy control

Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality

In this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the controller and the haptic device. When discussing the stability of the haptic system near its operating point, the original nonlinear system is modeled as a linear system with the time delay mentioned above. In addition, a suitable augmented Lyapunov–Krasovskii functional (LKF) with more integral forms is constructed and an auxiliary function-based integral inequality is applied to estimate the derivative of the proposed LKF. Then, a less conservative delay-dependent criterion in terms of the linear matrix inequality (LMI) is derived to calculate the delay margin for the haptic system. Finally, case studies are carried out based on a one degree of freedom haptic system. The results show that, compared with criteria in existing works, the proposed criterion can obtain more accurate results and require less calculation complexity, and, with the increase in virtual damping in a certain range, the stable upper bound of the haptic system increases at first and then decreases.

Evaluation of Delays-based Stability of LFC Systems in the Presence of Electric Vehicles Aggregator

In the integrated electrical systems, frequency control service considering the electric vehicle (EV) aggregators could lead to time-varying delay in load frequency control (LFC) schemes. These delays influence the LFC system efficiency, and in some situations, the lack of a clear choice of a control strategy considering the time-varying delays causes power system instability. Thus, this paper illustrates different time-varying delays based on the stability of an LFC system in the EV aggregators presence. The LFC's delay-dependent stability study is executed for finding the stability region and, stability criteria is suggested using the linear matrix inequality (LMI) method and Lyapunov-Krasovskii theory. Also, Wirtinger-based improved inequality and bounding lemma are applied to compute the greatest allowable delay in the LFC system, including the EV aggregators.