Stability Analysis Of Systems Research Articles

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.

Parametrised auxiliary function-based integral inequality for time delay system

ABSTRACT This paper employs two scalar parameters to extend auxiliary function-based integral inequality into a new formulations, say a parametrised auxiliary function-based integral inequality. Using these formulations, the constituent signals are utilised more efficiently by exploiting the interaction between them to reduce conservatism. Numerical example for stability analysis of linear systems with time-varying delay shows the improved performance of the proposed new formulations in terms of maximum delay bounds and decision variables.

Distributed Robust Learning-Based Backstepping Control Aided With Neurodynamics for Consensus Formation Tracking of Underwater Vessels.

This article addresses distributed robust learning-based control for consensus formation tracking of multiple underwater vessels, in which the system parameters of the marine vessels are assumed to be entirely unknown and subject to the modeling mismatch, oceanic disturbances, and noises. Toward this end, graph theory is used to allow us to synthesize the distributed controller with a stability guarantee. Due to the fact that the parameter uncertainties only arise in the vessels' dynamic model, the backstepping control technique is then employed. Subsequently, to overcome the difficulties in handling time-varying and unknown systems, an online learning procedure is developed in the proposed distributed formation control protocol. Moreover, modeling errors, environmental disturbances, and measurement noises are considered and tackled by introducing a neurodynamics model in the controller design to obtain a robust solution. Then, the stability analysis of the overall closed-loop system under the proposed scheme is provided to ensure the robust adaptive performance at the theoretical level. Finally, extensive simulation experiments are conducted to further verify the efficacy of the presented distributed control protocol.

Stability analysis and control synthesis of hybrid time-varying linear systems using a discretization-based approach

A strategy for stability analysis and control design concerning a class of hybrid linear time-varying (LTV) systems is proposed in this paper. First, the transition matrix of the system is computed and then used to formulate the stability analysis condition, unifying both the flows and jumps into a single continuous-time framework and resulting in a straightforward methodology for hybrid dynamics. Such condition is then adapted to yield the proposed synthesis techniques, capable of generating a time-varying state-feedback gain to stabilize the hybrid LTV system. A discretization procedure is then proposed for both analysis and synthesis conditions, resulting on a numerically suitable approach that allows the adaptation of any LTV discrete-time synthesis technique to deal with the considered hybrid LTV systems. Finally, to highlight the possibilities of the methodology, the conditions are adapted for the stabilization of sampled-data time-varying systems. Numerical examples illustrate the validity and potentialities of the proposed techniques.

Moving Bragg Solitons in a Dual-Core System Composed of a Linear Bragg Grating with Dispersive Reflectivity and a Uniform Nonlinear Core

The existence and stability of moving Bragg grating solitons are systematically investigated in a dual-core system, where one core is uniform and has Kerr nonlinearity, and the other is linear with Bragg grating and dispersive reflectivity. It is found that moving soliton solutions exist throughout the upper and lower bandgaps, whereas no soliton solutions exist in the central bandgap. Similar to the quiescent solitons in the system, it is found that when dispersive reflectivity is nonzero, for certain values of parameters, sidelobes appear in the solitons’ profiles. The stability of the moving solitons is characterized using systematic numerical stability analysis. Additionally, the impact and interplay of dispersive reflectivity, soliton velocity, and group velocity on the stability border are analyzed.

Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

Adaptive Terminal Sliding-Mode Synchronization Control with Chattering Elimination for a Fractional-Order Chaotic System

In this paper, an adaptive terminal sliding-mode control (ATSMC) method is proposed for the synchronization of uncertain fractional-order chaotic systems with disturbances. According to the sliding-mode control theory, a non-singular sliding surface is constructed. To overcome the chattering problem of ATSMC, a smooth term is used in the controller. In order to reduce the estimation error of an uncertain parameter, adaptive laws are designed to adjust the amplitude of the continuous function. Based on the Lyapunov stability theory, a stability analysis of the error system is performed to ensure that the tracking error eventually converges to the origin. The effectiveness and applicability of the proposed control strategy are verified using the simulation results.

Stability and stabilization of systems with a cyclical time-varying delay via delay-product-type looped-functionals

In this paper, the stability analysis and synthesis of systems with a cyclical time-varying delay are investigated. At first, the entire delay interval is divided into intervals of monotonically increasing and monotonically decreasing alternating cycles. Then, a Lyapunov-Krasovskii functional (LKF) with two delay-product-type looped-functionals is constructed based on different delay monotone intervals. For the generated quadratic function with respect to delay in the derivative of LKF, a matrix-injection-based method is utilized to obtain the negative-definite conditions of LKF’s derivative. A delay-dependent stability criterion with less conservatism is derived and the corresponding state-feedback control strategy is given consequently. Finally, a numerical example is utilized to show the superiority and the effectiveness of the proposed method, and a single-area power system under load frequency control is applied to verify the feasibility of the proposed control strategy.

Robust PID control of a tuned mass damper system and its stability analysis validation by Kharitonov and Edge theorems

ABSTRACT A robust control and stability analysis of a tuned mass damper attached to benchmark the model of mass-spring-damper system via different Kharitonov-related approaches, including the post-Kharitonov Edge Theorem, is presented in this paper. The control of uncertain parameters of the given system is demonstrated via robust Proportional-Integral-Derivative (PID) system tuning techniques in MATLAB. Usually, the Kharitonov theorem is sufficient to check the stability analysis of a controlled interval system. A detailed stability analysis of the given system by forming the Kharitonov rectangular parameter boxes and testing the positivity of Hurwitz determinants of the enclosed segments connecting opposite corners of the box is explained here. Stability checking is validated by the analysis based on the Hurwitz matrices of two Kharitonov polynomials. The multi-linear affine system model in the overall system plant is controlled and analysed via Edge theorem.

Research on space power supply utilizing series-parallel techniques

In the realm of space exploration, maintaining a stable and reliable power supply is crucial for the sustained and uninterrupted operation of artificial satellites. However, the unpredictable and often harsh space environment necessitates a redundant design for space power supplies to enhance overall reliability. In light of this, this paper introduces a full-bridge converter employing a series-parallel topology, which augments input voltage redundancy through a combination of serial and parallel connections. Furthermore, a dual-loop Proportional-Integral (PI) control feedback system has been devised, along with a comprehensive analysis of system stability to ensure the optimal performance of both output voltage and current. To validate the efficacy of the series-parallel topology and the feedback system, a complete circuit is constructed, and extensive simulations are carried out under diverse conditions.

Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

We apply known special functions from the literature (and these include the Fox H–function, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the G–function, the Fox–Wright function and the Meijer G–function) and fuzzy sets and distributions to construct a new class of control functions to consider a novel notion of stability to a fractional-order system and the qualified approximation of its solution. This new concept of stability facilitates the obtention of diverse approximations based on the various special functions that are initially chosen and also allows us to investigate maximal stability, so, as a result, enables us to obtain an optimal solution. In particular, in this paper, we use different tools and methods like the Gronwall inequality, the Laplace transform, the approximations of the Mittag-Leffler functions, delayed trigonometric matrices, the alternative fixed point method, and the variation of constants method to establish our results and theory.

Small Disturbance Stability Analysis of Onshore Wind Power All-DC Power Generation System Based on Impedance Method

The Onshore Wind Power All-DC Generation System (OWDCG) is designed to integrate with renewable energy sources by modifying the grid structure. This adaptation supports the grid infrastructure and addresses the challenges of large-scale wind power AC collection and harmonic resonance during transmission. Crucially, small disturbance stability parameters are essential for ensuring the system’s stable operation. Unlike conventional power systems, the OWDCG exhibits strong coupling between subsystems, accentuating the small disturbance stability issue due to the dynamic nature of its converter control system. The impedance method facilitates the decomposition of such systems into subsystems, offering insights into the destabilization mechanism through the lens of negative impedance contribution. This approach is conducive to conducting small disturbance stabilization analyses. To tackle this issue, the initial step involves deriving the input and output equivalent impedance models of the subsystem, considering the topological structure, control features, and operational dynamics of the OWDCG. Subsequently, the impact of circuit and control parameters on the system’s impedance characteristics and small-disturbance stability is examined through Bode diagrams and Nyquist curves. This analysis identifies critical parameters for small-disturbance stability, guiding the stable operation and parameter optimization of the OWDCG. The analysis highlights that the main control strategies for stability are the Modular Multilevel Converter (MMC) DC voltage control and the inner-loop current control gain. Validation of the theoretical findings is achieved through simulation results using PSCAD/EMTDC.

Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability

Lyapunov stability theory provides a powerful technique for stability analysis of dynamical systems, particularly for the stability of nonlinear dynamical system. This paper deals with the stability of fuzzy dynamical systems using a novel notion called granular fuzzy Lyapunov function. In order to analyze the stability, some new notions are introduced such as fuzzy equilibrium point, the ball of fuzzy state space, granular fuzzy 2-norm and etc. Based on the concept of fuzzy-number-valued function granular differentiability, two theorems are proved for calculation. Moreover, using granular fuzzy Lyapunov function, the granular fuzzy local stability theorem is proposed, and two definitions of exponential stability and like-Lyapunov stability are generalized. Finally, several examples are given to illustrate the proposed theorems.

Stability analysis of discrete-time delayed systems via matrix-injection-based transformation method for bivariate quadratic functions

In this paper, the stability analysis of discrete-time systems with a time-varying delay is studied. First, a selectable matrix-injection-based transformation lemma is proposed to guarantee the negative (or positive) definiteness of bivariate quadratic function. This lemma allows a selection of conditions that combine different delay sets, which is more relaxed than that in most previous studies. Then, an improved Lyapunov–Krasovskii functional (LKF) with delay-squared-product summation is given, which introduces extra cross-terms about delay-variation square for stability analysis. Considering the role of injection matrices in the proposed lemma, together with two types of allowable delay sets, four stability criteria are established. Finally, the less conservatism of the proposed criteria is verified by two numerical examples, which demonstrate the superiority of the presented methods.

Accurate Stability Analysis of Three-Phase Converter System Connected to Weak Grid under Coordinate System Transformation

This paper studies the simplified impedance criterion of the three-phase converter system in different coordinate systems. In addition, the influence of small signal stability of converter units under the weak grid is discussed in three-phase converter systems. Firstly, a small signal model of a three-phase grid-connected converter system is established based on the voltage and current double closed-loop control strategy in dq real coordinate system and the dynamic characteristics of SRF-PLL (Synchronous Reference Frame Phase-Locked Loop). Then, based on the coordinate transformation, the admittance models in the dq real coordinate system and the fb complex coordinate system are derived. Through the analysis of the admittance Bode diagram, the amplitude-frequency characteristics of the three-phase converter system have conjugate symmetry in the real coordinate system and diagonal conjugate symmetry in the complex coordinate system. Therefore, the three-phase symmetrical system can be stabilized only by drawing the Nyquist curve of the open-loop transfer function GHf or GHb. The three-phase asymmetric system can also be stabilized by drawing the Nyquist curve of the modified open-loop transfer function GHfM or GHbM . Finally, the simulation results show that the converter system loses stability when the transmission line impedance Lg = 0.6 pu. In this case, the three current decoupling terms will cause the system to lose stability, but the relative stability of the current reference value is the best, and the phase angle margin is −6.8°. Also, without considering the phase-locked loop dynamics, the system is in a steady state, otherwise, the system loses stability, and the system output current has a 39 Hz oscillation, which is consistent with the theoretical analysis results.

Build Borophite from Borophenes: A Boron Analogue Graphite.

Unlike graphene derived from graphite, borophenes represent a distinct class of synthetic two-dimensional materials devoid of analogous bulk-layered allotropes, leading to covalent bonding within borophenes instead of van der Waals (vdW) stacking. Our investigation focuses on 665 vdW-stacking boron bilayers to uncover potential bulk-layered boron allotropes through vdW stacking. Systematic high-throughput screening and stability analysis reveal a prevailing inclination toward covalently bonded layers in the majority of boron bilayers. However, an intriguing outlier emerges in δ5 borophene, demonstrating potential as a vdW-stacking candidate. We delve into electronic and topological structural similarities between δ5 borophene and graphene, shedding light on the structural integrity and stability of vdW-stacked boron structures across bilayers, multilayers, and bulk-layered allotropes. The δ5 borophene analogues exhibit metallic properties and characteristics of phonon-mediated superconductors, boasting a critical temperature near 22 K. This study paves the way for the concept of "borophite", a long-awaited boron analogue of graphite.

Robust stability analysis for uncertain systems with time‐varying delay via variable augmentation approach

AbstractThis paper investigates the problem of robust stability analysis for systems with time‐delays and time‐varying structured uncertainties. The variable augmentation approach and the free‐matrix‐based inequality are employed to retain the linear property of the estimation of the derivative of the Lyapunov–Krasovskii functionals. Moreover, with the use of the variable augmentation approach related to the time‐varying structured uncertainties, the time‐varying S‐Procedure combined with the time‐varying delay and its derivative is employed. As a result, less‐conservative robust stability conditions are derived. In addition, the merits of the augmentation of the time‐varying structured uncertainties over the traditional methods are theoretically demonstrated. Finally, two numerical examples are given to verify the benefits of the proposed methods.

Stability Analysis and Event-Triggered Control for IT2 Discrete-Time Positive Polynomial Fuzzy Networked Control Systems With Time Delay

Stability Analysis and Event-Triggered Control for IT2 Discrete-Time Positive Polynomial Fuzzy Networked Control Systems With Time Delay

Small-Signal Stability Analysis of Three-Phase Four-Wire System Integrated With Single-Phase PV Inverters Considering Phase to Phase Coupling

Small-Signal Stability Analysis of Three-Phase Four-Wire System Integrated With Single-Phase PV Inverters Considering Phase to Phase Coupling

Equivalence of Impedance Participation Analysis Methods for Hybrid AC/DC Power Systems

Participation analysis based on whole-system impedance models enables the root-cause stability analysis of large-scale power systems when state-space models are unavailable. To extend participation analysis to the hybrid AC/DC system, especially for the interlinking converter, this paper proposes two complementary methods, namely the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">direct method</i> and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">indirect method</i> . The direct method treats the interlinking converter as hybrid AC-DC port apparatus and the participation factor can be defined with the terminal hybrid AC-DC impedance matrix correspondingly. As for the indirect method, system equivalence can be made at the AC or DC terminal of the interlinking converter when impedance models within subsystems are unavailable such that preliminary knowledge of systems can be simplified. Importantly, the equivalence of these two methods on the observability of system components is revealed through theoretical analysis. The proposed impedance participation analysis methods are illustrated with a 4-bus hybrid AC/DC system, a modified 28-bus hybrid AC/DC system and a modified 96-bus hybrid AC/DC system. Numerical calculations and time-domain simulations are performed to validate the theoretical analysis.