Stability Criteria For Systems Research Articles

Enhancing Stability Criteria for Linear Systems with Interval Time-Varying Delays via an Augmented Lyapunov–Krasovskii Functional

This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability conditions for interval time-varying linear systems. In this work, the compositions of the LKFs are considered to enhance the feasible region of the stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality (WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality (LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. Then, simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in four examples. Four numerical examples show that the proposed Theorems 1 and 2 obtain less conservative results than existing outcomes. Particularly, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1 in some specific systems.

Master–slaves synchronization of teleoperation systems with the Try‐Once‐Discard protocol under event‐triggered communication

AbstractIn this paper, a class of single‐master‐multiple‐slaves (SMMS) bilateral teleoperation systems with the limitation of communication bandwidth is investigated. The signals are exchanged between the master and the slaves through delayed communication. Besides, to avoid data collisions, the Try‐Once‐Discard (TOD) scheduling protocol is utilized to decide which slave gets the network access at each triggered instant. A control algorithm with the event‐triggered mechanism is proposed to ensure the master–slaves synchronization. Furthermore, the closed‐loop system's stability criterion associated with the controller gains, the varying time delays' bounds, and the maximum transmission interval is established on the basis of the Lyapunov–Krasovskii analysis. Finally, the presented algorithm's performance is demonstrated by the simulation and experiment results.

Relaxed mixed convex combination lemmas: Application to stability analysis of time-varying delay systems

Stability analysis of time-varying delay systems is a fundamental issue, and reducing the conservatism of stability criteria is the key. The high-order Bessel-Legendre inequality together with appropriate Lyapunov-Krasovskii functional (LKF) has the potential to reduce conservatism, but the reciprocally convex and quadratic correlation terms of time-varying delay appear in LKF derivative. This paper proposes the relaxed mixed convex combination lemmas, in which the reciprocally convex combination lemma introduces delay square terms in the LKF derivative, and the quadratic convex combination lemma relaxes the negativity condition for quadratic polynomial functions. The less conservative stability criteria of systems with time-varying delay satisfying two cases are derived, making the delay upper bound larger, and the design degree of freedom higher. Finally, two well-known numerical examples are presented to demonstrate the superiority of the lemmas and criteria over the previous works.

A novel finite-time stability criteria and controller design for nonlinear impulsive systems

The issue of a novel finite-time stability and stabilization design for a class of nonlinear impulsive systems is discussed in this paper. In previous finite-time control designs for impulsive systems, the convergence rate of these control strategies is even less rapid than the exponential convergence rate when the initial state is distant from the origin. To overcome this problem, two sufficient conditions for the novel finite-time stability of impulsive systems are presented, in which the stabilizing impulses and the destabilizing impulses are considered, respectively. Meanwhile, the upper bound of the settling-time is evaluated. In addition, combining Lyapunov functions theory with impulsive control, we design a controller for impulsive dynamical systems to satisfy the novel finite-time stability. Finally, two simulation examples are given, in which the first example demonstrates the superiority of the proposed finite-time stability criterion for nonlinear impulsive systems by comparing it with traditional finite-time stability, and the second example verifies the effectiveness of the presented controller.

Eigenvalue spectra of finely structured random matrices.

Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are applicable in a myriad of different contexts. However, it is often assumed that all components of the complex system in question are statistically equivalent, which is unrealistic in many applications. Here we introduce the concept of a finely structured random matrix. These are random matrices with element-specific statistics, which can be used to model systems in which the individual components are statistically distinct. By supposing that the degree of "fine structure" in the matrix is small, we arrive at a succinct "modified" elliptical law. We demonstrate the direct applicability of our results to the niche and cascade models in theoretical ecology, as well as a model of a neural network, and a directed network with arbitrary degree distribution. The simple closed form of our central results allow us to draw broad qualitative conclusions about the effect of fine structure on stability.

Synchronous and non synchronous delay-dependent robust wide-area controllers for power system

Wide-area control is highly efficacious for maintaining sufficient damping of the low-frequency oscillations in the power system. The Wide-Area Measurement System (WAMS) provides wide-area signals to the control site through a communication channel. Even though the wide-area signal improved the dynamic behavior of the power system, a time delay usually exists during the transmission, which is unavoidable. The damping performance of the power system is degraded due to the time delay. In this paper, synchronized and non-synchronized feedback configurations are considered, and the time delay margin is calculated. The Lyapunov theory is adopted for investigating the synchronous and non-synchronous delay-dependent stability criteria for the power system. A lead–lag and a robust H∞ wide-area damping controller (WADC) are proposed to measure the delay margin for synchronized and non-synchronized delay feedback. The relationship between the damping performance and the delay margin is established. It is observed that a non-synchronous feedback-based controller can endure a larger time delay variation than a synchronous feedback-based controller. The nonlinear simulation is carried out to verify the effectiveness of the proposed controllers in Kundur’s two-area system and the IEEE-39 bus test system.

Privacy-preserving federated machine learning modeling and predictive control of heterogeneous nonlinear systems

Privacy preservation in data-driven modeling of a heterogeneous nonlinear system with multiple subsystems has become vitally important since communication data is vulnerable to cyber-attacks. This work develops a federated learning (FL) modeling and model predictive control (MPC) method for heterogeneous nonlinear systems with multiple subsystems to address privacy preservation and heterogeneity issues. The FL framework with two different neural network structures is developed to aggregate the submodels trained locally for the subsystems into a global model without sharing the local data with each other. Subsequently, a theoretical bound on the generalization error of the FL models is established using information theory. The closed-loop stability criteria of heterogeneous nonlinear systems under the FL-based MPC scheme are developed in an information-theoretical manner. Finally, a chemical process network is applied to demonstrate the effectiveness of the proposed FL modeling and FL-based MPC methods.

Stability and Stabilizability Criteria of Nonlinear Interval Systems

Stability and Stabilizability Criteria of Nonlinear Interval Systems

Stability and reliability analysis for broadband current array sensing system applied to GIS

Abstract In order to further improve the defect detection capability of gas insulated switchgear and avoid equipment faults, broadband current array sensing system is designed to simultaneously monitor the system status such as partial discharge, relative dielectric loss, and power frequency overvoltage. The dynamic model of the system is analysed, and based on which, the system state equation is obtained meanwhile fault observer is designed, and the system stability criterion under H ∞ condition is calculated. The reliability of the system under different packet loss rates is verified based on cloud models, and the principle of using appropriate electromagnetic compatibility to prevent packet loss rates below 50% is proposed.

Characterizations and Stability Criteria for the 2-Mode Markovian Switched Nonlinear Systems

Characterizations and Stability Criteria for the 2-Mode Markovian Switched Nonlinear Systems

Relaxed Stability Criteria for Time-Delay Systems: A Novel Quadratic Function Convex Approximation Approach

Relaxed Stability Criteria for Time-Delay Systems: A Novel Quadratic Function Convex Approximation Approach

Exponential synchronization of a class of quaternion-valued neural network with time-varying delays: A Matrix Measure Approach

This article investigates the exponential synchronization (ES) of quaternion-valued neural networks (QVNNs) with time-varying delays. Global ES has been studied using matrix measure techniques. Due to the incompatibility of quaternion multiplication, the QVNN system is first separated into four real-valued systems. Then ES is established in the master-response systems of QVNN by constructing a state feedback controller. The stability criteria for the error system of QVNN is then provided using the existing lemmas and the Halanay inequality. Additionally, it is no longer assumed that the activation functions are differentiable, which make the analytical process more concise. The viability of our findings are demonstrated using two numerical examples. The present theoretical findings have been confirmed in the first case, while the second example includes the use of QVNNs connected to associative memory to demonstrate their ability to restore real color image patterns properly.

A novel stability criterion and precise control for linear time delay systems based on regional configuration of the poles

This paper presents the concept of region stability and provides criteria for region stability of linear time delay systems, which can reveal the dynamic and steady-state performance of the systems more precisely. Corresponding design schemes for stabilization and tracking control that can accurately control various performance of time delay systems have also been explored. First, in the light of the connection between the poles and the dynamic properties of the system, the concept of region stability is given to describe the finer dynamic behavior of time delay systems. The criteria for the region stability are also presented. Second, the region stabilization methods are investigated, which can ensure that the system satisfies a certain dynamic performance by setting the eigenvalues in a certain convex region. Third, a precise tracking control of the linear time delay systems is addressed as an application of region stabilization. It can control the steady state performance and transient response of the tracking signal more precisely. Finally, three instances are provided to display the superiority of the new method for the performance indexes of the linear time delay systems.

Improved stability and stabilization criteria for multi-rate sampled-data control systems via novel delay-dependent states

This paper aims to obtain less conservative stability and stabilization conditions for sampled-data linear systems with multiple sampling rates. To this end, three novel delay-dependent states resulting from sampling are introduced in the augmented state, enabling the exploitation of the sawtooth-type characteristics of the sampling-induced delay in both stability and stabilization processes. Additionally, a novel discontinuous function is included in Lyapunov–Krasovskii-based functional to enhance the capacity to extract more information from specific sampling pattern for each state. Especially, to strengthen the interdependence among the components of the augmented state, supplementary zero equalities are incorporated into the stability analysis conditions. Furthermore, by including a novel weighted state derivative in the augmented state, this paper proposes an effective method that can transform the parameter-dependent stability conditions into stabilization conditions formulated in terms of linear matrix inequalities. Finally, the validity and practicality of the proposed method are demonstrated through two illustrative examples.

Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua’s circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm’s robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security.

Study of Stability Criteria of Automatic Control Systems By Multiparametric Aviation Objects

ABSTRACT This paper considers the comparative analysis of the physical and mathematical methods of the optimal operation of aviation objects’ automatic control systems, which is an urgent scientific and technical task. The paper also represents the corresponding stability criteria, depending on the operating conditions, and the influence of external factors that allows ensuring the automatic control systems’ reliable operation not only in normal circumstances, but also in the presence of probable disagreements. The scientific novelty of the research lies in developing new stability criteria by means of synthesising the influence of different factors and also the ability to ensure optimal functioning of the automatic control systems. Corresponding mathematical and computer models have been developed. The use of these models allows to determine the optimal stability criteria for control systems with parameters of a different physical nature and ensure reliable operation of electromechanical systems for general and special applications based on the current analysis. The research results are illustrated by corresponding mathematical models, engineering calculations and modelling of the optimal control limits depending on the influence of various factors. The simulation results coincide with the theoretical calculations, which indicates the consistency between the microprocessor-based and software of automatic control systems.

Stability criteria of random nonlinear systems with non‐instantaneous multiple impulse

AbstractThis paper comprehensively explores the stability analysis of random nonlinear systems subjected to random non‐instantaneous multiple impulses. The random non‐instantaneous multiple impulses refer to various impulsive intensities, with the type of impulse at each moment determined by a Markov chain. Drawing on the properties of stochastic processes, a series of stability criteria are developed for the random non‐instantaneous multiple impulsive systems within the constraint of fixed impulsive intervals. To validate the practicality of the proposed conceptual methods, the tracking control problem of network surface vessels under deception attacks is investigated, demonstrating feasibility through simulation results.

Model and Dynamic Analysis of a Three-Body Tethered Satellite System in Three Dimensions

The three-body tethered satellite system is a new potential technology for the purposes of orbital transportation. In contrast to conventional orbit transfer methods, this system is expected to transport space supplies to a predetermined orbital altitude without consuming fuel; however, the unwanted libration resulting from the Coriolis force acting on moving subsatellites may induce tumbling within the system. In order to analyze the strongly coupled characteristics of the libration motion and the variable-length tethers, a six-DOF dynamic model of the system based on Newton’s law is established. By utilizing the dynamic equations and stability criterion for linear systems, three equilibrium configurations of the satellite system with two constant-length tethers are given. The coupling characteristics of the libration angles are analyzed based on mechanical features and simulations. The results demonstrate that part of the libration energy can transfer from out-of-plane motion to in-plane motion during out-of-plane libration, but not vice versa or when in-plane libration occurs alone. Furthermore, the dynamic characteristic of this system with a predesigned deployment strategy is surveyed. This investigation reveals that such a strategy can rapidly suppress the out-of-plane libration motion while maintaining purely sinusoidal oscillations in the in-plane motion.

General single/multiple integral inequalities and their applications to stability of time-delay systems

This paper is concerned with the stability of time delay systems. A new type of multiple integral inner product and a new class of multiple integral inner product space are firstly introduced. Based on them, general single/multiple integral inequalities are developed, and some previous integral inequalities including single and multiple integral inequalities can be regarded as their special cases. Secondly, suitable Lyapunov–Krasovskii functionals (LKF) are constructed. On the basis of the proposed integral inequalities, the derivative of the LKF can be gauged more accurate than those in the literature. As a result, some improved stability criteria of time-delay systems are formulated in terms of linear matrix inequalities. Through two numerical examples, it is shown that these criteria can provide larger delay upper bounds than some existing ones, showing the effectiveness and superiority of the proposed method.

Supplemental Stability Criteria with New Formulation for Linear Time-Invariant Fractional-Order Systems

In this paper, new stability criteria for linear time-invariant fractional-order systems (LTIFOSs) based on linear matrix inequalities (LMIs) are derived. The solved variable of the existing LMI formulations is generalized to a complex one. In addition, based on the congruent transformation, a new LMI formulation is obtained, which is different from those in the existing literature. To deal with the above LMIs more conveniently with simulation software, the complex LMIs are converted to equivalent real LMIs. Finally, numerical examples are presented to validate the effectiveness of our theoretical results.