Stability Analysis Of Systems Research Articles

Memory State‐Feedback Control for a Linear System With Time‐Varying Delay Based on the Tuning Matrix Search Algorithm

ABSTRACTA multiple augmented Lyapunov function (MALF) is a function that includes more than one augmented matrix, allowing for a more precise evaluation of the relationships between different states within a system and facilitating the analysis of system stability. However, employing multiple augmented matrices can complicate the process of designing controllers. For this issue, this article proposes a controller synthesis algorithm to address the complexity of controller design resulting from multiple augmentation matrices. First, a memory state‐feedback control criterion with tuning matrices is derived by constructing an MALF. Second, a tuning matrix search algorithm is proposed to provide appropriate tuning matrices for the memory state‐feedback control criterion, leading to the determination of optimal controller gains. Finally, the effectiveness and advantage are verified by simulation of load frequency control for in the power system and control for a linear singular time‐delay system.

Robust Distributed Load Frequency Control for Multi-Area Power Systems with Photovoltaic and Battery Energy Storage System

The intermittent power generation of renewable energy sources (RESs) interrupts the balance between power generation and demand load due to the increased frequency fluctuation, which challenges the frequency stability analysis and control synthesis of power generation systems. This paper proposes a robust distributed load frequency control (DLFC) scheme for multi-area power systems. Firstly, a multi-area power system is constructed by integrating photovoltaic (PV) and battery energy storage systems (BESSs). Then, by employing the linear matrix inequality (LMI) technique, the sufficient condition capable of ensuring that the proposed controller satisfies H∞ robust performance in the sense of asymptotic stability is derived. Finally, testing is conducted on a four-area renewable power system, and results verify the strong robustness of the proposed controller against load disturbance and intermittence of RESs.

A Fast Chebyshev Collocation Method for Stability Analysis of a Robotic Machining System with Time Delay

A Fast Chebyshev Collocation Method for Stability Analysis of a Robotic Machining System with Time Delay

Stability and bifurcation analysis of a 2DOF dynamical system with piezoelectric device and feedback control

This study aims to demonstrate the behaviors of a two degree-of-freedom (DOF) dynamical system consisting of attached mass to a nonlinear damped harmonic spring pendulum with a piezoelectric device. Such a system is influenced by a parametric excitation force on the direction of the spring’s elongation and an operating moment at the supported point. A negative-velocity-feedback (NVF) controller is inserted into the main system to reduce the undesired vibrations that affect the system’s efficiency, especially at the resonance state. The equations of motion (EOM) are derived by using Lagrangian equations. Through the use of the multiple-scales-strategy (MSS), approximate solutions (AS) are investigated up to the third order. The accuracy of the AS is verified by comparing them to the obtained numerical solutions (NS) through the fourth-order Runge-Kutta Method (RK-4). The study delves into resonance cases and solvability conditions to provide the modulation equations (ME). Graphical representations showing the time histories of the obtained solutions and frequency responses are presented utilizing Wolfram Mathematica 13.2 in addition to MATLAB software. Additionally, discusses the bifurcation diagrams, Poincaré maps, and Lyapunov exponent spectrums to show the various behavior patterns of the system. To convert vibrating motion into electrical power, a piezoelectric sensor is connected to the dynamical model, which is just one of the energy harvesting (EH) technologies with extensive applications in the commercial, industrial, aerospace, automotive, and medical industries. Moreover, the time histories of the obtained solutions with and without control are analyzed graphically. Finally, resonance curves are used to discuss stability analysis and steady-state solutions.

Stability analysis of aperiodic impulsive delay systems using sum of squares approach

AbstractThe stability problem of aperiodic impulsive delay systems with unstable continuous and discrete dynamics is addressed in this article. New delay‐dependent stability conditions are proposed by employing a clock‐dependent Lyapunov–Krasovskii‐like functional composed of a Lyapunov–Krasovskii functional and a high‐order polynomial matrix function. The stability conditions are then solved using sum of squares programming techniques, yielding less conservative results than the looped‐functionals approach. Finally, the simulation results demonstrate the effectiveness of the results.

Dynamic stability analysis of the aircraft electrical power system in the more electric aircraft concept

This paper presents the modelling and analysis process of the electrical power management system on board an electrified aircraft conforming to the More/All Electric Aircraft concept. The main objective of the study is to assess the stability of the Electric Power Distribution System under different operational conditions, including the aspect of constant power loads. The paper describes the structure of the system, in which the key role is played by a synchronous generator and a three-phase rectifier converting alternating current AC into direct current DC. To solve the problem, modeling methods in the Matlab/Simulink environment were used, which enabled the analysis of the dynamic properties of the system and the assessment of stability under various types of loads. The obtained test results show that the presence of constant power loads can lead to instability in the EPDS system, manifested by voltage and current oscillations exceeding the standards specified in the MIL-STD-704E standard. The paper also provides tools for predicting system stability without the need to conduct full stability tests, which is important for the design of modern aviation power systems. The final section of the work presents the research results obtained and the resulting significant insights and practical conclusions.

Method for Determining the Conditions for Ensuring Stable Rearward Movement of a Semi-trailer Combination with Non-turning Semi-trailer Wheels

The efficiency of organising freight transport and using motor transport in a Smart City depends on a set of its properties, which in the process of operation determine its suitability for use in given operating conditions. Vehicles have different overall dimensions and designs, which determine their maneuverability and directional stability, their ability to make a curve-line movement in the city, as well as to move safely in reverse. Nowadays, tractor-trailer combinations with non-turning semi-trailer wheels are widely used for freight transport. Such a scheme of vehicle construction does not ensure its directional stability when reversing, which can lead to the folding of the tractor and semi-trailer and loss of mobility of the combination. In the absence of additional special systems, the driver controls the rearward movement of the road train using the steering wheel and rear-view mirrors, and the accuracy of delivery to the object depends on the level of the driver's training. The research of driver's reaction time spent on situation assessment, decision making, and realisation has been carried out. It has been revealed that with manual control, there are difficulties connected with training of drivers to estimate the parameters of movement and control of the road train, in particular, with the process of parking and its accurate delivery to the object. With the help of the developed mathematical model of the rearward movement of the road train and the proposed new turn control law, the research of maneuvering of the road train during its delivery to the object has been carried out and the results confirming the possibilities of building an automated system allowing to reduce the influence of the human factor on the parking process, as well as to reduce the time required to perform the maneuver have been obtained. The conducted analysis of system stability with the help of Routh–Hurwitz criterion has determined the conditions of providing stability of the system moving in reverse. The method of controlling the backward movement of the road train and the design of the device realising it has been developed. The results of simulation modeling allowed us to find the necessary values for the control law for the movement of road trains of different lengths, as well as the preferred variants of the initial positions of the road train for the realisation of its precise delivery to the object.

Adaptive predefined-time precise anti-unwinding attitude control for a spacecraft with inertia uncertainty

This paper proposes an adaptive predefined-time accurate anti-unwinding attitude controller for a spacecraft with uncertain inertia. The novelty of the proposed algorithm lies in that the spacecraft attitude error is regulated to exact zero after a predefined settling time, which is an explicit parameter in the control algorithm. A time mapping function containing the predefined settling time is introduced, thus transforming the time scale of the original attitude control system. Then a composite barrier Lyapunov function is constructed to avoid the unwinding phenomenon in the attitude control process, and an adaptive backstepping attitude controller is designed based on the attitude system in the new time scale. The stability analysis of the attitude system is carried out based on LaSalle-Yoshizawa theorem, and it is proved that the attitude quaternion and angular rate can converge to zero accurately within the desired predefined time without using the spacecraft inertia information. Numerical simulation results show the effectiveness and superiority of the proposed controller.

Slope stability/instability analysis of advanced nanocomposite reinforced column structure under mechanical loading via coupled Carrera unified formulation, layer-wise and Laplace transform approaches

This study presents a comprehensive investigation into the slope stability and instability of column structures made of Triply Periodic Minimal Surfaces (TPMS) under mechanical loading. TPMS structures, known for their high strength-to-weight ratio, are increasingly used in engineering applications, particularly in lightweight structures. However, their stability behavior under complex loading conditions remains largely unexplored. To address this gap, we employ a coupled approach integrating the Carrera Unified Formulation (CUF), the Layer-Wise (LW) theory, and Laplace Transform techniques. The CUF framework, known for its versatility in modeling structural behavior across different geometrical and loading configurations, is utilized to capture the mechanical response of the TPMS-based columns. The LW theory further enhances the model by accurately representing the through-thickness behavior, particularly crucial for layered or composite TPMS structures. Finally, the Laplace Transform approach is applied to efficiently solve the governing differential equations, reducing the computational complexity of time-dependent mechanical analyses. A parametric study investigates the influence of various geometrical parameters, material properties, and loading conditions on the stability of the structures. The results highlight the critical factors influencing slope stability, including the interplay between the TPMS geometry and material distribution. Moreover, the findings offer insights into failure mechanisms, providing a basis for optimizing the design of TPMS-based columns for enhanced mechanical performance. This work contributes to advancing the theoretical understanding of TPMS structures, offering novel methodologies for slope stability analysis in complex mechanical systems.

Analysis and Design of a Battery and Supercapacitor‐Based Propulsion System for Electric Vehicles

ABSTRACTThis work deals with the design and development of a dual source based propulsion architecture for electric vehicles. The converter utilized for the propulsion system is derived from a conventional CuK converter, which operates in a bidirectional power flow mode. The proposed propulsion system has two energy sources: a battery and a supercapacitor (SC). The proposed system has continuous input and output currents at low and high voltage sides, which improves the cycle life of hybrid energy storage (SC and battery) and the DC‐link capacitor. Further, the proposed converter has magnetic reduction compared to a conventional two‐input bidirectional CuK converter. Moreover, an effective and simpler control strategy (only one switch is pulse width modulated (PWM) operated at a time) has been developed for energy management between sources during charging (regenerative braking) and discharging (propulsion), which is effectively verified by simulation and experimental results. Further, a frequency domain (bode plot)‐based technique is used for controller design and stability analysis of the proposed system.

Stability analysis of quasilinear systems on time scale based on a new estimation of the upper bound of the time scale matrix exponential function

In this paper, the stability of quasilinear systems on time scale is analyzed based on a new estimation of the upper bound of the time scale matrix exponential function. First, some new upper bounds for the norm of the matrix exponential function eA(t,t0) are derived, where A is a regressive square matrix, t,t0∈T, T being a time scale. The matrix exponential function generalizes the usual matrix exponential as well as the integer power of a matrix. It is shown that the obtained bounds are more accurate compared to the existing bounds of the norm of the matrix exponential function. One of the upper bounds is then used for stability investigation of quasilinear systems evolving on arbitrary time domains.

Flutter margin research based on system stability analysis methods

Flutter margin research based on system stability analysis methods

Consecutive time‐intervals‐dependent looped functionals for stability analysis of linear systems with asynchronous sampling

Consecutive time‐intervals‐dependent looped functionals for stability analysis of linear systems with asynchronous sampling

A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur'e Systems With Actuator Saturation: A Hybrid Lyapunov Method.

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

Secure virtual coupling control of connected train platoons under cyber attacks

Virtual coupling of automated trains has emerged as a promising technology to enhance the operational efficiency and line capacity of railway transportation systems. However, the vulnerability of such systems to malicious cyber attacks poses a significant threat to their stability, reliability and applicability. This article addresses the challenge of ensuring secure virtual coupling control of connected train platoons subject to various cyber attacks, including false data injection attacks, denial-of-service attacks, and replay attacks. First, based on the low-dimensional and noisy sensor measurements, novel set-valued observers are designed for each follower train to estimate their inaccessible full longitudinal motion states despite uncertainties and unknown attacks and noises. Then, distributed secure attack-compensation-based virtual coupling control laws are developed to ensure the platoon's stability and resilience against cyber attacks. Additionally, formal stability analysis of the resultant estimation error system and platoon tracking error system is provided. Furthermore, two algorithms are presented to elaborate the offline observer and controller design process as well as their online implementation. Finally, based on the data of a realistic urban rail transit line, simulation experiments are conducted to validate the efficacy of the proposed theoretical findings.

On separability of semigroups: application to models of physics and discrete optimization

Nilpotent semigroups are used in various fields of physics to model processes like system decay in quantum mechanics, state transitions in statistical mechanics, and simplifying dynamical systems. They also assist in optimizing control processes. The set of nilpotent matrices forms a semigroup and plays a key role in Jordan decomposition, which has many physical applications. In quantum mechanics, the Jordan form helps analyze linear operators on Hilbert spaces, especially with systems involving eigenvalue multiplicities. In vibration analysis, it aids in studying normal modes of mechanical systems with degenerate frequencies. Additionally, Jordan decomposition simplifies control theory for linear time-invariant systems, stability analysis in dynamical systems, and the behavior of coupled oscillators, as well as solving systems of linear differential equations. Certainly, the semigroup theory has even more applications in theoretical computer science: suffice it to say, for example, that some authors identify semigroups and finite automata. In this paper, we address the problem of P-separability of semigroups with respect to three key predicates: equality-separability, divisibility-separability, and subsemigroup-separability, achieved through homomorphisms into a nilpotent semigroup. We present some significant results that advance the understanding of these concepts.

A high-frequency reduced-order model for parameters optimization of AC/DC distribution systems considering random disturbances

Accompanying the rapid development of AC/DC distribution systems, along with the random disturbances introduced by a significant number of distributed generations and loads, the difficulty of system stability analysis has increased. The phenomenon of DC bus voltage instability has become severe, affecting the safe and stable operation of power systems. This paper focuses on the research of multi-terminal AC/DC distribution systems. A reduced-order method for multi-terminal distribution systems is proposed. Through parameter equivalent transformation, the system model is simplified while maintaining its dynamic characteristics. Parameter sensitivity analysis is utilized to identify key parameters influencing the system’s dynamic behavior, achieving an analytical expression of the system’s dynamic characteristics. And stability domain analysis is applied to delineate the variations in system dynamic behavior and responses to random disturbances under different parameter settings. Then a multi-parameter optimization method is designed to enhance system stability while achieving fast system response. Finally, theoretical analysis is validated through software simulation and hardware-in-the-loop experiments.

Stability Analysis and Stabilization of General Conformable Polynomial Fuzzy Models with Time Delay

This paper introduces a sum-of-squares (S-O-S) approach to Stability Analysis and Stabilization (SAS) of nonlinear dynamical systems described by General Conformable Polynomial Fuzzy (GCPF) models with a time delay. First, we present GCPF models, which are more general compared to the widely recognized Takagi–Sugeno Fuzzy (T-SF) models. Then, we establish SAS conditions for these models using a Lyapunov–Krasovskii functional and the S-O-S approach, making the SAS conditions in this work less conservative than the Linear Matrix Inequalities (LMI)-based approach to the T-SF models. In addition, the SAS conditions are found by satisfying S-O-S conditions dependent on membership functions that are reliant on the polynomial fitting approximation algorithm. These S-O-S conditions can be solved numerically using the recently developed SOSTOOLS. To demonstrate the effectiveness and practicality of our approach, two numerical examples are provided to demonstrate the effectiveness and practicality of our approach.

The Dynamic Behavior of a Stochastic SEIRM Model of COVID-19 with Standard Incidence Rate

This paper studies the dynamic behavior of a stochastic SEIRM model of COVID-19 with a standard incidence rate. The existence of global solutions for dynamic system models is proven by integrating stochastic process theory and the concept of stopping times, together with the contradiction method. Moreover, we construct appropriate Lyapunov functions to analyze system stability and apply Dynkin’s formula and Fatou’s lemma to handle stopping times and expectations of stochastic processes. Notably, the extinction study provides mathematical proof that under the given system dynamics, the total population does not grow indefinitely but tends to stabilize over time. The properties of the diffusion matrix are harnessed to guarantee the system’s stationary distribution. Conclusively, numerical simulations confirm the model’s extinction outcomes.

Optimal Control of Underdamped Systems: An Analytic Approach

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.