Conditions For Stability Of Systems Research Articles

Synchronization for fractional-order neural networks with unbounded delays

This paper deals with synchronization analysis problem for a class of fractional-order neural networks with unbounded delays. Using the Lyapunov function method combined with fractional Halanay inequality, we derive a novel sufficient condition for asymptotic stability of the error system resulting in two neural networks are synchronized. The obtained conditions are given in terms of linear matrix inequalities, which therefore can be efficiently checked. A numerical example is proposed to illustrate the effectiveness of the obtained results.

New input‐to‐state stability conditions of linear systems with interval time‐varying delays and their application to power systems

AbstractIt is commonly believed that the Lyapunov‐Krasovskii functional method plays an important role in obtaining input‐to‐state stability conditions of systems with interval time‐varying delays. For a system with an interval time‐varying delay, an appropriate functional should be constructed during applying the method. Nevertheless, the delay has an interesting property that the delay in different delay intervals can have varying impacts on the system. In a way, the property is not considered adequately for the Lyapunov‐Krasovskii functional method, which may give rise to conservative conditions. This article proposes a new input‐to‐state stability analysis method by taking advantage of the ignored property. When the new method is adopted, multiple functionals are constructed for the delay in the different delay intervals. This means that the multiple functionals method is more applicable in practice than the Lyapunov‐Krasovskii functional method. With the help of the proposed method, new input‐to‐state stability conditions for linear delay systems are derived. A numerical example is presented to show that the obtained conditions are effective. At last, the newly derived conditions are applied to power systems with delayed load frequency control schemes.

Hierarchical stability conditions for linear systems with interval time-varying delay

This paper proposes the hierarchical stability conditions for linear systems with an interval time-varying delay. In the matter of the delay, the upper and lower bounds are restricted, but there is no constraint on its derivative. Firstly, based on the state vectors and multiple integral state vectors involved in the delay-related generalized free-matrix-based integral inequalities (GFIIs), the hierarchical Lyapunov-Krasovskii functional (LKF) candidates are constructed. Then, the GFIIs are applied for the approximation of the integral quadratic terms, which will introduce the delay related nonlinear terms in the LKF differential. Next, the novel adjusted matrix-valued high and odd degree polynomial negative definite conditions (NDCs) are provided to acquire the hierarchical linear matrix inequality (LMI) conditions and cope with the nonlinear terms introduced by the GFIIs. Eventually, the advantages of the obtained stability conditions are checked through some numeric examples.

Financial system stability in Indonesia and its relationship with economic growth before and during the Covid-19 pandemic

The purpose of this study is to assess the condition of financial system stability in Indonesia both before and during the Covid-19 pandemic and to look at its relationship with economic growth. This study develops six sub-sector groups described in 19 indicators in order to assess the condition of the financial system. Quarterly data for 6.5 years from Quarter I 2016 to Quarter II 2022 was evaluated. To assess the condition of the financial system, this study uses a composite index approach with the normalized max-min method. The correlation analysis method is used to assess the relationship between the index of financial system conditions and economic growth. The results showed that during the pandemic, there was a more significant increase in pressure on financial conditions than before the pandemic. The financial system instability index during the pandemic in the second quarter of 2020 was 3 times higher than the average and more than 5 times higher than the same quarter in 2019. In addition, the relationship between the financial condition index and economic growth is at 0.77 (strong category). The implication is this research can provide insight to the government, financial institutions, and the public regarding the condition of financial system stability before and during the Covid-19 pandemic. This research suggests that the government should control credit restructuring policies during the pandemic and strengthen financial institutions. This research has limitations in terms of objects that only include conventional financial institutions. Further studies can use other objects such as Islamic financial institutions.

Stability analysis of complex-valued stochastic neural networks with multi-time-delay and parameter uncertainty

This paper investigates the examination of global asymptotic stability pertaining to uncertain complex-valued stochastic neural networks (UCVSNNs) with multiple time delays. This paper employs the real-imaginary separated activation function to establish an equivalence between complex-valued neural networks (CVNNs) and two real-valued activation functions, representing the real and imaginary parts respectively. This equivalence is utilised to analyse the original UCVSNNs model in a comprehensive manner. The global asymptotic stability of the studied UCVSNNs model is ensured by constructing an appropriate Lyapunov-Krasovskii generalised function and applying the I t o ^ formula, linear matrix inequality (LMI) and other analytical techniques to derive the system stability and other sufficient conditions. In the meanwhile, we provide two numerical examples to demonstrate the reliability and benefit of the discovered results.

Stability for nonlinear delay systems: Self-triggered impulsive control

This paper studies the stability problem of nonlinear delay systems in the framework of self-triggered impulsive control (STIC), where a class of self-triggered mechanisms is designed based on comparison approach. Different from the traditional event-triggered impulsive control (ETIC), in this paper the next impulse instant can be predicted at the previous impulse instant, and there is no need for state monitoring between two adjacent impulse instants. Under the proposed STIC strategy, some sufficient conditions for non-Zeno behavior and asymptotical stability of nonlinear delay systems are presented, respectively. Finally, two numerical examples are carried out to illustrate the effectiveness of the theoretical results.

Design and implementation for the state time-delay and input saturation compensator of gas turbine aero-engine control system

In order to obtain desired steady-state and transient performance of a gas turbine aero-engine during its operation, a usual way is to control the engine to operate in a manner close to its physical limits. The thermodynamic performance of a gas turbine aero-engine varies greatly within a wide working envelope, affected by factors such as engine performance degradation, actuator response lag and combustion time-delay. When the engine works in extreme conditions, for example rapid acceleration, some phenomena such as over-speed, over-temperature and over-pressure may occur. For this reason, various restrictions are often set in the engine control system to ensure safety during its operation, which are often realized by the form of saturation. In this paper, a compensation structure for gas turbine aero-engine state time-delay and input saturation is proposed. At first, the problems frequently occurred in the gas turbine aero-engine control system are investigated. And the gas turbine aero-engine control model is derived based on a thermodynamic non-linear model and its linearization model is established, together with its designed compensation structure. Differing from the existing technologies, a combination of dynamic system input saturation feedback and static state time-delay feedback is adopted in the proposed model. Then, the saturated nonlinearity and time-delay characteristic are introduced as convex combinations in the stability analysis. The local stability conditions of the closed-loop system are obtained by using Lyapunov–Krasovskii functionals and linear matrix inequalities (LMIs). Finally, hardware-in-loop (HIL) experiments are conducted to verify the feasibility of the proposed compensation method.

Improved Event-Triggered Dynamic Output Feedback Control for Networked T-S Fuzzy Systems With Actuator Failure and Deception Attacks.

This article addresses the problem of event-triggered dynamic output feedback controller design for networked Takagi-Sugeno (T-S) fuzzy systems subject to actuator failure and deception attacks. In order to save network resources effectively, two event-triggered schemes (ETSs) are introduced to test whether the measurement output and control input are transmitted under network communication. While the ETS brings advantages, it also leads to a mismatch between the premise variables of the system and the controller. To solve this problem, an asynchronous premise reconstruct method is considered, which relaxes the condition of the previous results that the premises of the plant and the controller are synchronous. Furthermore, two crucial factors, including actuator failure and deception attacks, are taken into consideration simultaneously. Then, the mean square asymptotic stability conditions of the resultant augmented system are derived by utilizing the Lyapunov stability theory. Besides, controller gains and event-triggered parameters are co-designed with the help of linear matrix inequality techniques. Finally, a cart-damper-spring system and a nonlinear mass-spring-damper mechanical system are presented to verify the theoretical analysis.

Novel Stability Conditions for Nonlinear Monotone Systems and Consensus in Multiagent Networks

We introduce a novel definition of monotonicity, termed “type-K” in honor of Kamke, and study nonlinear type-K monotone dynamical systems possessing the plus-subhomogeneity property, which we call “K-subtopical” systems after Gunawardena and Keane. We show that type-K monotonicity, which is weaker than strong monotonicity, is also equivalent to monotonicity for smooth systems evolving in continuous-time, but not in discrete-time. K-subtopical systems are proved to converge toward equilibrium points, if any exists, generalizing the result of Angeli and Sontag about convergence of topical systems' trajectories toward the unique equilibrium point when strong monotonicity is considered. The theory provides an new methodology to study the consensus problem in nonlinear multi-agent systems (MASs). Necessary and sufficient conditions on the local interaction rule of the agents ensuring the K-subtopicality of MASs are provided, and consensus is proven to be achieved asymptotically by the agents under given connectivity assumptions on directed graphs. Examples in continuous-time and discrete-time corroborate the relevance of our results in different applications

Boundary feedback stabilization of an unstable cascaded heat–heat system with different reaction coefficients

The present paper addresses a boundary stabilization problem for a cascaded heat–heat system with different reaction coefficients. A sufficient and necessary condition about two reaction coefficients of the cascaded heat–heat model is found to guarantee the controllability of the coupled system. Based on modal decomposition method, a feedback control is proposed to stabilize the coupled system. Sufficient conditions for exponential stability and well-posedness of the closed-loop systems are derived via the Lyapunov method. The performance is validated by the numerical simulation, which illustrates the efficiency of the proposed control scheme.

Exponential stability of linear systems under a class of Desch–Schappacher perturbations

In this paper, we investigate the uniform exponential stability of the system where the unbounded operator is the infinitesimal generator of a linear semigroup of contractions in a Hilbert space and is a Desch–Schappacher operator. Then we give sufficient conditions for exponential stability of the above system. The obtained stability result is then applied to prove the uniform exponential stabilization of some bilinear partial differential equations.

Optimal analysis of a multi-server queue with preprocessing time and replenishment inventory

ABSTRACT Recently, e-commerce has had the advantage of lower rental expenses. Convenient online payment has rapidly grown and provides a great business opportunity for enterprises. Inventory management plays a critical role in the competitiveness of most electronic business enterprises. Before the products hit the store shelves or are available online to customers, the quantity and quality of the products should be confirmed and inspected. Thus, in addition to the replenishment lead time, the preprocessing time has essential effects on inventory management. To reduce the inventory cost and determine a proper replenishment policy, we propose a multi-server inventory queue with a preprocessing time, which is seldom mentioned by the existing studies. The steady-state probabilities, system stability conditions, and expressions of several critical system characteristics are derived. Subsequently, the operating cost function is developed to determine the optimal reorder point and an appropriate number of servers with the minimum cost. The established numerical results and sensitivity analysis help managers identify critical variables and enhance operational efficiency.

Output-Feedback Control of Interconnected Nonlinear Systems With Both State and Input Delays Based on Truncated Prediction

In this paper, we investigate decentralized output-feedback control of interconnected nonlinear systems with both state and input delays. Unlike existing related works, in this paper, both the state delays and the input delay of each subsystem are unknown and different from each other. In order to achieve global asymptotic stability of the interconnected nonlinear system based on output feedback, we construct a finite-dimensional observer based on the output information to asymptotically estimate the state information. Simultaneously, based on a truncated prediction of the system state over the delay period, a novel decentralized observer-based output-feedback controller is proposed for each subsystem. Then, under the framework of Lyapunov-Krasovskii functional, a set of conditions for the global asymptotic stability of the closed-loop system is determined. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.

Mismatched disturbance compensation enhanced robust H∞ control for systems with nonvanishing uncertainties/disturbances

AbstractThis article proposes a robust control method based on disturbance observer techniques for systems subject to mismatched uncertainties/disturbances. In the existing composite robust control methods with disturbance compensation, only matched uncertainties/disturbances, that is, the uncertainties/disturbances acting on the same channels as the control inputs, are feedforward compensated, while the mismatched ones are only attenuated in a conservative manner. It should be highlighted that if the mismatched uncertainties/disturbances are nonvanishing, the controller generally requires excessive control energy to suppress the effects of uncertainties/disturbances, where the control gains must be designed to ensure robust properties at the expense of sacrificing nominal tracking and/or stabilization performances. To address this problem, this article further introduces the compensation of mismatched uncertainties/disturbances into the robust control. Moreover, to attenuate the effects of observation errors, sufficient conditions for the asymptotic and robust stability of error systems are established. Finally, the proposed controller is applied to a DC–DC buck converter system feeding constant power load. Experimental results confirm its feasibility and efficiency.

A Decentralized Control Strategy for Series-Connected Single-Phase Two-Stage Photovoltaic Grid-Connected Inverters

Currently, most of the series inverter control methods rely on communication, which greatly reduces the reliability of the system and increases the cost. To address the above problems, this paper proposes a decentralized control strategy for series-connected single-phase two-stage grid-connected photovoltaic (PV) inverters. By improving the traditional droop control, the frequency and phase of the output voltage of each inverter unit are consistent and self-synchronized with the power grid while relying only on local independent control, and each unit realizes maximum power point tracking (MPPT). At different light intensities, each series-connected unit can quickly track the new maximum power point while still maintaining self-synchronization between the units. The system stability is analyzed via the small signal method, and sufficient conditions for system stability are obtained. Finally, the simulation results verify the correctness and effectiveness of the proposed control strategy.

Stability analysis and L1-gain characterization of positive sampled-data systems

In this study, the positive stability and [Formula: see text]-gain characterization problem are investigated for positive sampled-data systems. By constructing a new sampling-period-dependent copositive Lyapunov functional, and introducing the free weight matrix method to remove the single integral term, sufficient conditions for the asynchronous stability of the positive sampled-data system are established. Furthermore, system disturbances that occur frequently in engineering are taken into account. Conditions for robust stability of positive sampled-data systems that satisfy [Formula: see text]-gain performance are developed in the form of the linear programming technology. A numerical example and a practical simulation based on a communication network model are provided to illustrate the rationality and application of the theoretical results.

The Impact of Banking Competition on Bank Financial Stability: Evidence from ASEAN 5 Countries

In the era of the global economy, increasing banking competition will encourage an increase in banking transactions and activities. Banking transactions and activities will affect a country's financial stability. The purpose is to obtain the nonlinear effect of banking competition on financial stability at a specific regime. Previous research assumed that this impact applies to every economic regime. The impact of banking competition on financial stability can change at certain regime levels. Nonlinear impact occurs according to the regime. The method is based on a nonlinear threshold regression model. The researchers obtained the data from five ASEAN countries. The findings of this research are in-depth information about the financial system stability model. Analysis of the effect of variance supports the inconsistency of the effects found by several previous researchers. Practical implications are aimed at policymakers to make different decisions at the GDP level, CAR and Liquidity. The economic regime in each country is different, so this analysis is constructive for policymakers to see the conditions of banking competition and financial system stability at a certain regime level. The originality article systematically offers an analysis that assumes the effect can change at a certain regime level.JEL Classification: E5, G15, G01, G32, C24

Event‐based reduced‐order H∞$H_{\infty }$ estimation for switched complex networks based on T‐S fuzzy model

AbstractThis paper investigates the design of a reduced‐order filter for a specific class of switched complex network systems with time‐varying delays. To handle the nonlinear components of the complex network, a T‐S fuzzy model is employed to convert them into a set of linear components. To tackle the issue of heavy network load, a memory‐based adaptive trigger mechanism is proposed. In this study, a reduced‐order state estimator is designed using the T‐S fuzzy model. To demonstrate the exponential stability of the error system, a suitable Lyapunov function is constructed based on the Lyapunov stability principle. The parameter matrix of the reduced‐order estimator is determined using the linear matrix inequality and convex linearization method. Additionally, a sufficient condition for the exponential stability of the error system at the suppression level is provided. Finally, the feasibility of the proposed scheme is validated through a simulation experiment.

Collaborative adaptive cruise control and energy management strategy for extended-range electric logistics van platoon

This paper improves the economy of the extended-range electric logistics van (ERELV) platoon from two aspects of cooperative adaptive cruise control (CACC) and energy management strategy (EMS). Based on the vehicle-to-everything (V2X) communication, to improve the economy of heterogeneous vehicle platoon CACC system, a distributed model predictive controller (DMPC) with stability, comfort, and the economy as optimization goals are designed. The sufficient conditions for the asymptotic stability of the vehicle platoon closed-loop system are obtained by Lyapunov stability analysis. The multi-agent deep reinforcement learning (MADRL) algorithm is used to solve the EMS of the ERELV platoon. Under the framework of centralized training distributed execution (CTDE), the experience of all agents can be obtained during training, and the actions can be output only according to their local observation states during execution. The simulation results show that the designed ecological cooperative adaptive cruise control (Eco-CACC) effectively balances the stability and economy of a heterogeneous vehicle platoon. Taking dynamic programming (DP) as the benchmark, compared with the single-agent algorithm, EMS based on a multi-agent deep deterministic strategy gradient (MADDPG) algorithm can achieve a near-optimal solution while significantly improving the learning efficiency.

A novel approach of decentralized H∞$H_{\infty }$ fuzzy filtering for nonlinear large‐scale systems with uncertain interconnections

AbstractThis paper proposes, a novel decentralized fuzzy filter design for nonlinear large‐scale systems with uncertain interconnections. Based on Takagi–Sugeno (T–S) fuzzy model, the error system is represented by filter error and filter state variables, and the filtering problem is defined. By using the Lyapunov functional, the stability condition of the error system with performance is obtained to solve the filtering problem, and its sufficient condition is converted into the linear matrix inequality (LMI) formats. Furthermore, the decentralized fuzzy filter design technique is also presented for the non‐measurable premise variable case. Finally, an example is provided to verify the effectiveness of the proposed decentralized fuzzy filtering techniques.