Delay-dependent Stability Analysis Research Articles

Improved delay-dependent stability analysis of digital filters with generalized overflow arithmetic

This paper introduces a new set of conditions that establish Input-to-State Stability (ISS) for digital filters with external disturbance input and time-varying delays, all within the context of generalized overflow arithmetic. A unique augmented Lyapunov function and a novel summation inequality are applied to formulate a new criterion for ISS. This criterion assesses the ISS of digital filters in the presence of external disturbance, enabling the identification of asymptotic stability even in the absence of such disturbance. The criteria are developed using linear matrix inequalities (LMIs). The efficacy of the results is demonstrated through three numerical examples, highlighting that the proposed criteria are less conservative than some recent results.

Delay-dependent exponential stability of highly nonlinear stochastic functional switched systems: an average dwell time approach

The delay-dependent exponential stability of stochastic functional switched systems (SFSSs) with highly nonlinear coefficients is investigated in this paper. By virtue of the mode-dependent average dwell time (MDADT) technique, the existence of global solution and qth moment exponential stability is studied without linear growth condition (LGC). Both of drift and diffusion coefficients have functional terms which can embody many existing delay cases, e.g. constant delay, time-varying delay and distributed delay, etc. By employing common/multiple Lyapunov function method, sufficient delay-dependent stability criteria of qth moment exponential stability are proposed. The MDADT condition reveals the positive role of switching signal in the delay-dependent stability analysis. Finally, an example is given to validate our theoretical results.

Delay-dependent stability analysis for load frequency control systems with time-varying delays

This paper introduces a delay-dependent criterion that addresses both computational accuracy and efficiency in dealing with delay-dependent stability challenges within multi-area load frequency control (LFC) systems. Firstly, the traditional power system LFC model is decomposed into delay-related and delay-independent parts using a model reconstruction technique. Subsequently, an augmented Lyapunov–Krasovskii functional (LKF) is formulated, focusing on the delay-related part of the model. The double integral component within the derivative of the LKF is constrained using the parameter-dependent slack matrices approach, resulting in a less conservative stability criterion. Finally, the proposed result is validated through case studies. Simulation results demonstrate that the proposed stability criterion significantly improves computational accuracy while maintaining better validity compared to existing approaches. Moreover, compared to the traditional LFC model, the reconstructed model offers substantial computational efficiency improvements, albeit with a slight decrease in computational precision.

Participation of Electric Vehicles in a Delay-Dependent Stability Analysis of LFC Considering Demand Response Control

Today, time-varying delays may result from a communication network’s engagement in frequency control services. These delays have an impact on the effectiveness of the load frequency control (LFC) system, which can occasionally lead to power system instability. The electric vehicle (EV) can be used as a beneficial source for the LFC system with the development of demand-side response due to its vehicle-to-grid capacity. Although demand response control has certain advantages for the power system, communication networks used in LFC systems result in time delays that reduce the stability of the LFC schemes. A stability study of an LFC system, comprising an EV aggregator with two additive time-varying delays, is demonstrated in this work. An enhanced Lyapunov–Krasovskii functional (LKF), which incorporates time-varying delays using the linear matrix inequality approach, is used to perform a delay-dependent stability analysis of the LFC to determine the stability zone and criterion. In conclusion, the efficiency of the proposed stability criterion is validated by making use of the thorough simulation findings.

Stability delay margin computation of multi-area load frequency control system with electric vehicle using critical eigenvalue tracing method

This work presents the delay-dependent stability analysis using eigenvalue tracing method for the multi-area load frequency control system that includes both electric vehicles aggregator (LFC-EVs) and incommensurate time delays in each control area. The LFC-EVs systems face inevitable communication time delays that affect the frequency stability. Although communication infrastructures are necessary to maintain system stability and reliability, a large amount of delay exceeding the allowable limit leads to system instability. In this study, stability delay margin values of a time-delayed LFC-EVs system are computed by a simple method finding the critical eigenvalues. By tracing eigenvalue loci of a transformation matrix, the method easily determines critical eigenvalues on the imaginary axis and obtains stability regions in time delay space. Stability delay margins depicted as a stability region in the delay space are determined for various system parameters and verified by time-domain simulations. Results indicate that more accurate stability delay margins are obtained as compared to ones using Lyapunov–Krasovskii Functionals with different linear matrix inequalities.

Delay-Dependent Stability Analysis and Design of Input-delayed Systems by Smooth Sliding Mode Control: Lagrange Theorem Approach

A new smooth sliding mode control design methodology based on Lagrange mean value theorem is proposed for stabilization of single input delayed systems. The Lagrange mean value theorem as a basic theorem of calculus is used for the design of linear sliding mode time-delay controller for the first time. This controller satisfies the sliding condition using a Zhou and Fisher type continuous control law eliminating the chattering effect. The constructive delay-dependent asymptotically stable sliding conditions are obtained by using the augmented Lyapunov-Krasovskii functionals and formulated in terms of simple (4x4)-matrix inequality with scalar elements. Developed design approach can be extended to robust stabilization of sliding system with unknown but bounded input delay. The maximum upper bounds of delay size can be found by using simple optimization algorithms. Helicopter hover control is considered as a design example for illustrating the usefulness of smooth sliding mode approach. Unstable helicopter dynamics are successfully stabilized by using linear sliding mode time-delay controller. For example, settling time is about 20 sec. Therefore, simulation results confirmed the effectiveness of proposed design methodology. Apparently, the proposed method has a great potential in design of time-delayed controllers.

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

This paper concentrates on the robust stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay. Firstly, by using a suitable Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems is proposed. Then, based on the above stability conditions, the robust delay-dependent and order-dependent stability conditions for the uncertain systems are discussed. Moreover, in order to stabilize the nominal and uncertain systems, state feedback controllers are also derived with the help of the presented stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.

Delay-Dependent Stability Analysis of Interfered Digital Filters with Time-Varying Delay and Saturation Nonlinearities

Delay-Dependent Stability Analysis of Interfered Digital Filters with Time-Varying Delay and Saturation Nonlinearities

Computation of Delay-Dependent Stability Regions for Electric Power Systems with Time Delay

Bu çalışma, bir özdeğer izleme yöntemi kullanarak güç sistem dengeleyici (GSD) ve otomatik gerilim regülatörü (OGR) içeren zaman gecikmeli jeneratör uyarma kontrol sisteminin zaman gecikmeleri düzleminde kararlılık bölgesini elde etmeyi ve zaman gecikmesine bağlı kararlılık analizini incelemektedir. Elektrik güç sistemlerinde gerilim ve frekans kararlılığının sürdürülmesi bakımından haberleşme alt yapısına ve ölçme sistemlerine ihtiyaç duyulmaktadır. Ancak, haberleşme alt yapısı ve ölçme sistemlerinden dolayı sistemin dinamik davranışını ve kararlılığını olumsuz etkileyen zaman gecikmeleri meydana gelmektedir. Bu çalışmada, jeneratör uyarma kontrol sisteminin durum denklem modellerini kullanarak özdeğerlerini ve bu özdeğerlere karşılık gelen zaman gecikmesi değerlerini belirleyen bir yöntem kullanılmıştır. Ayrıca, bu gecikme değerleri kullanılarak gecikmeye bağlı bir kararlılık bölgesi elde edilmiştir. Kararlılık analizleri için, GSD ve OGR içeren tek makineli sonsuz baralı (TMSB) bir güç sistemi seçilmiştir. Gecikmeye bağlı kararlılık bölgelerinin doğruluğu, zaman düzleminde gerçekleştirilen benzetim çalışmaları ve zaman gecikmeli sistemlerin köklerini kompleks düzlemde hesaplayan QPmR (the quasi-polynomial mapping-based root finder) algoritması ile gösterilmiştir.

Accurate Distributed Secondary Control for DC Microgrids Considering Communication Delays: A Surplus Consensus-Based Approach

The state-of-the-art dynamic consensus-based microgrid (MG) secondary controls suffer from the communication delay effect. Specifically, the system could not converge to the desired operating points with time-delayed communications. Such deviations are hard to detect in a decentralized manner and could destabilize the system. This paper proposes an accurate distributed secondary controller for DC MGs based on the surplus consensus algorithm. The proposed controller achieves accurate proportional power sharing and average voltage regulation among distributed generators (DGs) with the presence of variable and bounded communication delays. A surplus consensus-based observer is developed. The developed observer is proved robust against variable and bounded communication delays; it tracks the average of a group of dynamic states with zero steady-state deviations, which cannot be done using the conventional dynamic consensus-based observer. The convergence speed of the developed observer is analyzed and a parameter design procedure is presented. Moreover, the delay-dependent stability analysis of DC MG operation with the proposed secondary controller is derived. The marginal delay that leads the system to instability is calculated. At last, the performance of the proposed secondary controller and the developed stability analysis are validated under various scenarios using MATLAB/Simulink.

Delay-Dependent Positivity and Stability Analysis of Discrete-Time Systems With Delay

In this letter, delay-dependent positivity and stability conditions, which are crucially different from existing delay-independent ones, are derived for discrete-time systems with time-varying delay. By utilizing a special property called non-oscillatory behavior of solutions of scalar difference equations with delays, the proposed conditions are formulated in terms of linear programming settings. The efficiency of the obtained results is illustrated by a numerical example with simulations.

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

This paper is concerned with the stability analysis of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. This paper aims to derive a delay and nonlinear function bound dependent asymptotical stability criterion with less conservatism. Firstly, a new Lyapunov functional with several augmented terms, including extra free matrices and overflow nonlinear function, is constructed such that it has a relaxed positive condition. Then, for bounding the summation term arising in the forward difference of Lyapunov functional, a new lemma is developed to introduce the terms for linking the delayed states and the overflow nonlinear function, the Wirtinger-based summation inequality and several zero-value terms are applied to add more cross terms. As a result, a stability criterion with less conservatism is established and its conservatism. Finally, several numerical examples are given to illustrate the advantages of the proposed method.

Delay margin computation of load frequency control system with demand response and constant communication delays

The paper aims to present a comprehensive delay-dependent stability analysis technique of a networked single area Load Frequency Control (LFC) systems integrated with demand response. Demand Response (DR) has been an integral part of power system control and operation. The time-delays in LFC schemes are due to the utilization of communication channels for signal transmission among the various sub-systems and control center. The deterioration of the dynamic performance of the system is the most feasible effect of time-delays and at the worst these delays lead to instability. Therefore, the computation of delay margins for a stable operation of the single-area LFC system with DR control is crucial. A less conservative stability criterion using Lyapunov approach is derived in linear matrix inequality framework for determining the stability of closed loop LFC system under study. The stability criterion is tested for different subsets of the controller parameters and participation factors using standard benchmark system. Through extensive simulation results, the analytical results are validated. The time domain simulation results indicate the effectiveness of the analytical results.

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.

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.

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.

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.

Delay-dependent Stability Analysis Considering Dynamic Demand Response and Electric Vehicle Aggregator Integration in Two-Area Load Frequency Control Systems

Delay-dependent Stability Analysis Considering Dynamic Demand Response and Electric Vehicle Aggregator Integration in Two-Area Load Frequency Control Systems

Stability Analysis of Systems With Time-Varying Delay via Improved Lyapunov–Krasovskii Functionals

This paper is concerned with the delay-dependent stability analysis of linear systems with a time-varying delay. Two types of improved Lyapunov-Krasovskii functionals (LKFs) are developed to derive less conservative stability criteria. First, a new delay-product-type LKF, including single integral terms with time-varying delays as coefficients is developed, and two stability criteria with less conservatism due to more delay information included are established for different allowable delay sets. Second, the delay-product-type LKF is further improved by introducing several negative definite quadratic terms based on the idea of matrix-refined-function-based LKF, and two stability criteria with more cross-term information and less conservatism for different allowable delay sets are also obtained. Finally, a numerical example is utilized to verify the effectiveness of the proposed methods.