Stability Analysis Of Systems Research Articles

Stability analysis of single-machine infinite bus system with renewable energy sources using sine cosine chimp optimization

Stability analysis of single-machine infinite bus system with renewable energy sources using sine cosine chimp optimization

Stability analysis for stochastic nonlinear systems with state-dependent switching and time-delay

The stability of stochastic nonlinear systems with time-delay and state-dependent switching is studied in this paper. Firstly, system maximal solution is constructed and further extended as the global solution under certain mild conditions. Secondly, several Krasovskii-type stability and Razumikhin-type theorems are proposed by uniformly asymptotically stable functions (UASFs). These stability criteria overcome some stringent constraints associated with Lyapunov functional/functions. Finally, the theoretical findings are validated through two simulation examples.

Decentralized and performance-constrained state-estimated fuzzy control for nonlinear differential-algebraic interconnected systems

This paper introduces a decentralized and mixed performance-constrained state-estimated fuzzy control strategy designed for nonlinear differential-algebraic interconnected systems. Initially, the approach employs a Takagi-Sugeno (T-S) fuzzy model to approximate these complex systems. To address potential limitations within the interconnected systems, a Proportional-plus-Derivative (PD) state control method is integrated into the proposed control scheme. Additionally, an observer is constructed to estimate system states, enhancing the feasibility of the control method. System stability analysis is conducted using the free-weighing Lyapunov function approach, allowing designers to customize the weight matrix for desired control performance and facilitate controller design. Subsequently, a fuzzy controller is developed to ensure stability and meet both Passive-H∞ Performance (PHP) and H2 Control Performance (HCP) criteria. Finally, the effectiveness of the proposed design approach is validated through simulation results.

Stability analysis of inerter-based n-DOF vibration systems containing semi-active switched elements

Stability analysis of inerter-based n-DOF vibration systems containing semi-active switched elements

Stability analysis of fractional difference equations with delay.

Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order difference," can also have a long-time memory. Therefore, the fractional difference equations with delay are an appropriate model in a range of systems. Even so, there are not many detailed studies available related to the stability analysis of fractional order systems with delay. In this work, we derive the stability conditions for linear fractional difference equations with an arbitrary delay τ and even for systems with distributed delay. We carry out a detailed stability analysis for the cases of single delay with τ=1 and τ=2. The results are extended to nonlinear maps. The formalism can be easily extended to multiple time delays.

Small-Gain and Small-Angle Conditions for Feedback Stability Analysis of Linear Stochastic Systems

Small-Gain and Small-Angle Conditions for Feedback Stability Analysis of Linear Stochastic Systems

An investigation into the stability of helicopter control system under the influence of time delay using an improved LKF

This paper presents an improved Lyapunov-Krasovskii functional (LKF)-based stability analysis of time-delay systems (TDS) and its application to helicopter control systems. A novel LKF is proposed for the stability analysis of linear TDS after thoroughly examining the effects of each integral associated with a general class of LKF. The suggested stability results in the form of linear matrix inequalities (LMIs) are obtained using the Wirtinger-based integral inequality (WII), reciprocally convex combination lemma (RCCL), and extended reciprocally convex matrix inequality (ERCMI). Numerical examples are utilized to evaluate the impact of the presented theorems on stability. The proposed theorems are then used to examine the stability of helicopter control systems, and the results of these stability analyses are verified using a laboratory model of a helicopter control system.

An enhanced looped-functional framework for stability analysis of sampled-data systems

This paper enhances the looped-functional framework for sampled-data systems by using continuous Lyapunov functionals instead of xT(t)Px(t). The continuous Lyapunov functionals exploit the maximum allowable sampling interval compared with the traditional Lyapunov function xT(t)Px(t) in the conventional looped-functional framework. The enhanced looped-functional framework ensures the negativeness of the continuous Laypunov functionals concerning the sampling instants and guarantees the stability of the sampled-data systems. Based on these continuous Lyapunov functionals, this paper constructs novel Lyapunov functionals with the looped-functional which not only exploits all available vectors related to sampling intervals but also introduces an additional interval which is zero at t=tk+1. Also, this paper proposes the stability criteria based on the enhanced looped-functional framework for the sampled-data systems with the asynchronous and synchronous samplings, respectively. The numerical examples show the effectiveness of the proposed framework.

Multiple Vehicles and Traction Network Interaction System Stability Analysis and Oscillation Responsibility Identification

Multiple Vehicles and Traction Network Interaction System Stability Analysis and Oscillation Responsibility Identification

Stability analysis of stochastic differential systems with state‐dependent delay subject to average‐delay impulses

In this paper, we study the stochastic weak local exponential stability of stochastic differential systems with state‐dependent delay (SDD) subject to average‐delay impulses by using Lyapunov–Krasovskii functional and stochastic analytical skill. Unlike time‐dependent delay discussed in the previous literature, we introduce SDD in impulsive stochastic differential systems, where SDD is a stochastic variable associated with system state, consequently leading to an indeterminate delay boundary. Our findings reveal that when destabilizing delayed impulses satisfying specific conditions are generated, the stability of stochastic differential systems with destabilizing delayed impulses and stable continuous stochastic dynamics can still be maintained. Additionally, if stable delayed impulses satisfy certain conditions, stability of the systems under consideration can also be achieved, irrespective of the stable status on the continuous stochastic dynamics. Finally, two examples are given to demonstrate the validity of theoretical results.

Innovative Approach to Enhance Stability: Neural Network Control and Aquila Optimization Integration in Single Machine Infinite Bus Systems

This paper highlights the need to improve the stability of single-machine infinite-bus (SMIB) systems, which is crucial for maintaining the dependability, efficiency, and safety of electrical power systems. The changing energy environment, characterized by a growing use of renewable sources and more intricate power networks, is challenging established stability measures. SMIB systems exhibit dynamic behavior, particularly during faults or unexpected load variations, requiring sophisticated real-time stabilization methods to avert power failures and provide a steady energy supply. This paper suggests a complex approach that combines power system stability analysis with a neural network controller enhanced by the Aquila optimization algorithm (AOA) to address the dynamic issues of SMIB systems. The study shows that the AOA-optimized neural network (AOA-NN) controller outperforms in avoiding disruptions and attaining speedy stabilization by exhaustively examining electrical, mechanical, and rotor dynamics. This method improves power system resilience and operational efficiency as demands and technology expand.

Fault detection based on a residual intervals multigenerator for nonlinear systems

This paper is devoted to sensor fault detection for nonlinear systems using an interval multiobserver based on uncoupled multimodel. This proposed interval multiobserver is used to detect the faults through residual intervals multigenerator. The [Formula: see text] performance technique is introduced to improve the accuracy of the sensor fault detection. The stability analysis of the fault detection system is carried out using Lyapunov approach under LMI(s) formulation. A numerical simulation example is used to highlight the efficiency of the proposed residual intervals multigenerator and the robustness of the fault detection strategy.

Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case

The robust asymptotic stability problem for fractional-order linear systems with commensurate time delays (FOSCDs) and structured perturbations is investigated in this manuscript. Based on the properties of Kronecker products and μ-analysis, the necessary and sufficient conditions are given to guarantee the asymptotic stability of FOSCDs. Then, the necessary and sufficient conditions for the robust asymptotic stability of FOSCDs with structured perturbations are investigated. To reduce the computing complexity and deal with the problems of systems with larger dimensions, a sufficient condition on the robust asymptotic stability of FOSCDs with structured perturbations is given based on the properties of Kronecker products and 2-norm transformations. Finally, several examples are illustrated to test the effectiveness of the proposed results.

An approach to nonlinear optimisation via set stabilisation of dynamical systems with an application to synchronous machines

An approach to constraint nonlinear optimisation is proposed, where the variables of the objective function and of the constraint function belong to the state of a nonlinear dynamical system. A nonlinear closed-loop feedback system is designed, whose solutions converge to a target set consisting of the optimal points of the underlying optimisation problem. The feedback law for the control input of the nonlinear dynamical system is designed by exact linearisation of a dynamical formulation of a first-order optimality condition. For the problem formulation and the stability analysis of the nonlinear closed-loop feedback system, the notion of V-detectability is considered. An application to energy-optimal feed-forward torque control for different types of synchronous machines is presented, which demonstrates the usefulness of the method. In this regard, anisotropic permanent magnet synchronous machines and electrically excited synchronous machines are covered.

Outlier-resistant non-fragile observer-based fuzzy boundary control for interconnected nonlinear PDE systems

This paper investigates an observer-based boundary controller design for interconnected nonlinear partial differential equation (PDE) systems. First, the Takagi–Sugeno (T–S) fuzzy model is adopted to accurately describe the target systems. Then, boundary measurements are employed to reduce the number of sensors. Next, considering the phenomenon of abnormal interference that may lead to measurement outliers and observer parameters’ uncertainties, an outlier-resistant non-fragile observer expressed by a saturation function is designed to guarantee the desired control objectives. Moreover, the boundary control approach is employed to trade-off the cost of system design and system performance. Furthermore, utilizing the membership function-dependent Lyapunov functions and free-weight matrixes, sufficient conditions ensuring the closed-loop systems’ exponential stability are obtained while decreasing the conservativeness of the system stability analysis. Finally, the proposed method’s feasibility and effectiveness are validated by an example.

An efficient iterative method for matrix sign function with application in stability analysis of control systems using spectrum splitting

The goal of this study is to construct a novel iterative method to compute the matrix sign function using a different approach. It is discussed that the new method is globally convergent and asymptotically stable. It achieves the sixth order of convergence and only requires five matrix–matrix multiplications. The obtained results are extended to compute the number of eigenvalues of a matrix in a specified region of the complex plane. This is done by performing appropriate sequence of matrix sign computations. An application of this technique has been discussed in stability analysis of linear time‐invariant dynamic systems in control theory. Numerical results have been given to justify the effectual performance and superiority of the proposed method. Matrices of various sizes have been considered for this purpose.

A Robust Switching Control Strategy for Three-Phase Voltage Source Converters with Uncertain Circuit Parameters

This study proposes a novel double closed-loop robust control strategy based on a power switching affine model of three-phase voltage source converters (VSCs). The aim is to overcome the challenges posed by inaccurate mathematical models, complex controller configurations, indirect switching control, and performance degradation under circuit parameters uncertainty or load variation in conventional methods. These conventional methods rely on linearization models, duty ratio regulation, and pulse width modulation (PWM) technologies. The contributions of work are the following: (1) A two-dimensional (2D) power switching affine model is constructed without any approximation or averaging. (2) The proposed approach achieves direct switching control of three-phase VSCs, eliminating the need for complex rotation coordinate transformation, PWM, and phase locking loop (PLL), which are utilized in traditional control methods. (3) The rigor of the system stability analysis is enhanced based on the 2D power switching model compared to the existing three-dimensional (3D) current switching model. (4) A simple control structure with only two control parameters is employed to address circuit parameter uncertainties. The effectiveness and superiority of the proposed method is validated through simulation and experimental comparison results.

Stability analysis of a three-dimensional system of difference equations with quadratic terms

AbstractThis study is involved with a class of three-dimensional system of difference equations incorporating quadratic term, which naturally extends and improve several results in the literature. Firstly, we demonstrate the existence of fixed points, the boundedness, persistence and invariance of positive solution of the mentioned system. Later, for this system, we give the global asymptotic stability at fixed point and the rate of convergence result which play an important role in the discrete dynamical systems. And lastly, some numerical examples are given to validate the effectiveness and feasibility of the theoretical findings.

Stability analysis for nonautonomous impulsive hybrid stochastic delay systems

In this paper, the problems on the existence and uniqueness, and the input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are considered. The existence and uniqueness for the global solution of such systems is studied by using the Lyapunov function, the theory of stochastic analysis, and the function of the impulsive density. In order to overcome the difficulty stemming from the simultaneous presence of the indefinite derivative for the Lyapunov function, the bounded external disturbances, and a nonnegative and bounded time-varying delay, one impulsive generalized Halanay inequality of integral version is established. The input-to-state stability, the integral input-to-state stability, the stochastic input-to-state stability and the eλt(λ>0)-weighted input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are investigated, respectively. One example is provided to illustrate the effectiveness of the theoretical results obtained.

Stability analysis of hybrid integrator-gain systems: A frequency-domain approach

The hybrid integrator-gain system (HIGS) has been introduced recently with the aim to overcome fundamental limitations of linear time-invariant (LTI) control systems. To support the analysis and design of HIGS-based controllers, in this paper a novel frequency-domain condition for stability analysis of the feedback interconnection of an LTI system and HIGS is presented. Compared to existing frequency-domain stability conditions such as the one extending the circle-criterion, the condition presented in this paper exploits explicit knowledge regarding HIGS’ switching strategy, thereby potentially providing a significantly less conservative condition. In particular, the novel condition in this paper guarantees the existence of a quadratic Lyapunov function that does not need to be positive definite within the full state space. The proposed condition can be verified graphically in a manner that is reminiscent of the classical Popov plot, as will be illustrated in an experimental case-study.