Sufficient Stability Criterion Research Articles

Stabilization for 2-D switched T–S fuzzy systems under the state-dependent switching

This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.

Tube-based MPC strategy for load frequency control of multi-area interconnected power system with HESS

With the rapid development of power generation technology and the increasing demand from power users, multi-area interconnected power systems have become a development trend. This article proposes a new robust tube-based model predictive control strategy (MPC) for multi-area interconnected power systems with hybrid energy storage systems (HESS), based on the application of HESS to optimize the performance of load frequency control in power systems. The proposed strategy is mainly based on a new robustness constraint, which effectively handles uncertain disturbances within interconnected power system by compressing the disturbance invariant set. This strategy effectively alleviates the problems caused by inconsistency in multi-area interconnection modes. In addition, a sufficient stability criterion is derived to ensure the robust stability of the system, even under uncertain disturbances. By modeling a four-area interconnected power system with HESS, the frequency fluctuations of different methods are compared and discussed in each area. Based on the constructed software-in-the-loop setup, the effectiveness and feasibility of the proposed strategy are verified by experiments.

Delay-dependent exponential stability of highly nonlinear stochastic functional switched systems: an average dwell time approach

The delay-dependent exponential stability of stochastic functional switched systems (SFSSs) with highly nonlinear coefficients is investigated in this paper. By virtue of the mode-dependent average dwell time (MDADT) technique, the existence of global solution and qth moment exponential stability is studied without linear growth condition (LGC). Both of drift and diffusion coefficients have functional terms which can embody many existing delay cases, e.g. constant delay, time-varying delay and distributed delay, etc. By employing common/multiple Lyapunov function method, sufficient delay-dependent stability criteria of qth moment exponential stability are proposed. The MDADT condition reveals the positive role of switching signal in the delay-dependent stability analysis. Finally, an example is given to validate our theoretical results.

Exponential Stability of Impulsive Stochastic Neutral Neural Networks with Lévy Noise Under Non-Lipschitz Conditions

In this paper, the exponential stability issue of stochastic impulsive neutral neural networks driven by Lévy noise is explored. By resorting to the Lyapunov-Krasovskii function that involves neutral time-delay components, the properties of the Lévy process, as well as various inequality approaches, some sufficient exponential stability criteria in non-Lipschitz cases are obtained. Besides, the achieved results depend on the time-delay, noise intensity, and impulse factor. At the end of the paper, two numerical examples with simulations are presented to demonstrate the effectiveness and feasibility of the addressed results

Practical exponential stability and applications of switched homogeneous nonlinear systems with external inputs and impulses

The practical exponential stability of switched homogeneous nonlinear systems (SHNS) with external inputs and impulses is studied in this paper, which includes two types of continuous-time systems and discrete-time systems. Specifically, we add a kind of nonnegative impulses which is consistent with the switching behaviours for the systems. We first study switched homogeneous positive nonlinear systems (SHPNS) case, then we extend the SHPNS to a time-varying SHNS case. The primary difficulty of this research is the estimation of Lyapunov function value at switching-impulse points under the coupling effects of synchronous switches and state jumps. By employing the max-separable Lyapunov function approach, we present new sufficient stability criteria and design new switching-impulse signals, and successfully establish the new relation between the average dwell time parameter and impulse strength. Then, we apply the obtained results to the time-varying vehicle formation model with impulses. At last, four examples are given to demonstrate the feasibility of our results, which includes the specific algorithm verification process.

Sliding mode control of phase-type T-S fuzzy stochastic semi-Markov jump systems

In this paper, the sliding mode control (SMC) problem of phase-type semi-Markov jump systems (S-MJSs) is studied using Takagi-Sugeno (T-S) fuzzy technology. A novel integral-type sliding surface with artificial delay has been constructed and applied for the first time to phase type S-MJSs, reducing system conservatism and enhancing control performance. Firstly, this paper presents sufficient criteria for the robust random stability of these systems by utilizing model transformation methods, supplementary variable techniques, and modal-dependent Lyapunov-Krasovskii function methods. Secondly, the sliding mode controller is designed using matrix technology. Finally, the effectiveness of this method is demonstrated through a simulation example involving a single-link robotic arm, and the comparison results show the merits to the existing achievements.

Asynchronous output feedback quantized sliding mode dissipative control for Markovian jump time-delay systems with generally bounded transition rates

This article figures out the asynchronous output feedback sliding mode dissipative control issue for Markovian jump delay systems (MJDSs) with uncertain parameters and external disturbances. Different from the massive methods of constructing sliding mode surfaces (SMS), a new dynamic output feedback (DOF) integral SMS is developed, where the SMS is composed of a virtual controller with quantized output and the controller is asynchronous with the system mode. Meanwhile, the reachability of the SMS is guaranteed. In addition, the transition rates (TRs) considered in this paper are generally bounded, which means that the designed method applies to the more general case of TRs, such as fully known and partially unknown TRs. The sufficient criteria of stochastic stability and strict dissipation for the MJDSs are deduced. The design scheme of the controller gain matrix is proposed by the linear matrix inequality (LMI) technique. Finally, two examples are shown to demonstrate the effectiveness and feasibility of the designed technique.

Memory sampled-data control design for attitude stabilization of uncertain spacecraft with randomly missing measurements

This paper focuses on stabilizing the attitude of the rigid spacecraft under the sampled-data control design technique with constant communication delay. The system dynamics with model uncertainty (perturbation) and missing measurements are considered. The aim is to design a desirable attitude control that ensures the stabilization of the rigid spacecraft with an optimal H∞ performance level. A novel Lyapunov–Krasovskii functional is developed, incorporating looped characteristics, for the proposed study on the rigid spacecraft model by developing relevant new terms. Making use of the Lyapunov function as well as free-matrix-based integral inequality, sufficient stability criteria are established to assure the stability of the rigid spacecraft model. Furthermore, the desired sampled-data control gain matrices are acquired through the solution of linear matrix inequalities, which guarantees the asymptotic stability of the rigid spacecraft model. Finally, the numerical simulation demonstrates the efficacy of the theoretical study proposed for the rigid spacecraft model.

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.

Commutator of the Caputo fractional derivative and the shift operator and applications

In this paper, we study the commutator of the Caputo fractional derivative and the shift operator. Consequently, we sharpen the recent (Diethelm and Tuan, 2022) on the separation of solutions to fractional equations. As a byproduct, we also obtain the sub and super multiplicative laws of Mittag-Leffler functions, which play an essential role in our approach to fractional Halanay type inequalities. Furthermore, by utilizing the estimate of the commutator, we provide an upper bound with an exact decaying rate for the separation of solutions to delay fractional equations under a flexible condition. This upper bound can be seen as a generalization of previous fractional Halanay type inequalities with bounded delay, which improves both (Wang and Zou, 2019) and (Huong et al., 2023). Finally, we gain practical sufficient criteria for the (strict) Mittag-Leffler stability and finite-time attractivity for a class of delay fractional equations. Some concrete examples are examined to illustrate these results.

Intermittent Sampled-Data Control for Local Stabilization of Neural Networks Subject to Actuator Saturation: A Work-Interval-Dependent Functional Approach.

This article is concerned with the local stabilization of neural networks (NNs) under intermittent sampled-data control (ISC) subject to actuator saturation. The issue is presented for two reasons: 1) the control input and the network bandwidth are always limited in practical engineering applications and 2) the existing analysis methods cannot handle the effect of the saturation nonlinearity and the ISC simultaneously. To overcome these difficulties, a work-interval-dependent Lyapunov functional is developed for the resulting closed-loop system, which is piecewise-defined, time-dependent, and also continuous. The main advantage of the proposed functional is that the information over the work interval is utilized. Based on the developed Lyapunov functional, the constraints on the basin of attraction (BoA) and the Lyapunov matrices are dropped. Then, using the generalized sector condition and the Lyapunov stability theory, two sufficient criteria for local exponential stability of the closed-loop system are developed. Moreover, two optimization strategies are put forward with the aim of enlarging the BoA and minimizing the actuator cost. Finally, two numerical examples are provided to exemplify the feasibility and reliability of the derived theoretical results.

Robust State-Estimator-Based Control of Uncertain Semi-Markovian Jump Systems Subject to Actuator Failures and Time-Varying Delay

This note presents a reformed state-estimator-based adaptive control strategy for uncertain delayed semi-Markovian jump systems (DSMJS) via sliding mode technique. In comparison to most literature results requiring exact prior knowledge of system time-delay, a linear state estimator not linking any control inputs is developed to cope with the case with unknown state delays. By virtue of the acquired state estimation, the establishment of both a new switching surface of linear-type and the involved adaptive controller is provided, and the devised controller could not only admit the assigned SSL's reachability in limited time but also operate on the DSMJS as desired despite the hidden actuator failures and unknowable time-delays. Also, a new sufficient stochastic stability criterion serving as a crucial solution to the control parameters of the resultant plant is inferred. The method also holds in a similar fashion for uncertain plants with no time-delays and/or no switching case. Eventually, the raised method is verified by numerical examples.

Exponential synchronization of delayed coupled neural networks with delay-compensatory impulsive control

This paper studies the exponential synchronization problem for a class of delayed coupled neural networks with delay-compensatory impulsive control. A Razumikhin-type inequality involving some destabilizing delayed impulse gains and a new idea of delay-compensatory that shows two critical roles for system stability are presented, respectively. Based on the constructed inequality and the presented delay-compensatory idea, sufficient stability and synchronization criteria for globally exponential synchronization (GES) of coupled neural networks (CNNs) are presented. Compared with existing results, the uniqueness of the presented results lies in that impulse delays can be fetched and integrated to compensate for instantaneous unstable impulse dynamics caused by destabilizing gains. Moreover, constraints between system delay and impulsive delay are relaxed, and the interval of impulses no longer constrains the system delay. Comparisons and a practical application are given to demonstrate the superior performance of the presented novel control methods

Stability analysis of Boolean networks: An eigenvalue approach

This article investigates the stability of probabilistic Boolean networks (PBNs) and switched Boolean networks (SBNs). To begin with, a unique Boolean network is presented with both stochastic signal and switching signal. It is then converted to algebraic form using semi-tensor product. An important concept named “existed path” is proposed, and further a novel method based on eigenvalue and trace-based method is used to derive some necessary and sufficient stability criteria for the first time. Moreover, these criteria are extended to include ordinary PBNs and SBNs. Finally, several examples are given to illustrate the main results.

Necessary and Sufficient Conditions for Stabilizing an Uncertain Stochastic Multidelay System

We focus on the problem of asymptotically mean-square stabilization in discrete-time stochastic systems that exhibit plant uncertainty, multiple input delays, and multiplicative noises. Our innovative contributions are described as follows. First, we employ a reduction method to transform the original model into a delay-free auxiliary system, and establish an equivalent proposition for stabilization based on this reformulation. On the basis of the reformulated model, we propose two stabilization criteria for the uncertainty-free case, including both Lyapunov-type and Riccati-type criteria. More generally, we extend the stabilization result to the uncertain model, and propose a necessary and sufficient stabilization criterion utilizing matrix homogeneous polynomials. Finally, we explore the existence and uniqueness of a delay margin under certain structural restrictions, and provide a closed-form representation of this margin.

Necessary and sufficient criteria for existence, regularity, and asymptotic stability of enhanced pullback attractors with applications to 3D primitive equations

We introduce several new concepts called enhanced pullback attractors for nonautonomous dynamical systems by improving the compactness and attraction of the usual pullback attractors in strong topology spaces uniformly over some infinite time intervals. Then we establish several necessary and sufficient criteria for the existence, regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which are expected to be applied to many kinds of nonautonomous PDEs. These abstract results are applied to the famous 3D primitive equations modeling the large-scale ocean and atmosphere dynamics. We establish the existence, regularity and asymptotic stability of the enhanced pullback attractors for the nonautonomous primitive equations in [Formula: see text] and [Formula: see text] when the forces satisfy some mild conditions. The uniform pullback asymptotic compactness of the solution operators in [Formula: see text] and [Formula: see text] are established by deriving the uniform “flattening effects” of the solutions in [Formula: see text] and the uniform [Formula: see text]-Hölder continuity of the solutions from [Formula: see text] to [Formula: see text] with respect to the initial data, respectively. Our approaches are applicable to prove the existence of global attractors for the autonomous primitive equations in [Formula: see text] provided [Formula: see text].

Analytical investigation of factors affecting small-signal stability of grid-connected VSC

This paper provides an analytical investigation of the small-signal stability of the grid-connected voltage source converter (VSC) as well as the impacts of the system resistances. The dynamic model of the studied system is first established, and the characteristic function is derived from the linearized model. Based on the characteristic function, the analytical relationships between the system resistances and the dominated pole are obtained utilizing the analytical sensitivity approach. It is found that the line resistance can provide positive damping for the oscillation mode, improving the system stability, while the converter resistance will worsen the system stability. Generally, the line resistance has an evident more substantial impact on the stability of the grid-connected VSC than the converter resistance. The stability analysis results of the grid-connected VSC conducted by ignoring the system resistances are conservative. Ulteriorly, the characteristic function is simplified by neglecting the system resistances, and a sufficient and analytical stability criterion is established from the simplified characteristic function using the Routh Judgement. It exhibits the constraint condition among controller parameters, electrical distance and operation conditions for ensuring system stability. Moreover, the power transmission limitation of the converter affected by the controller parameters and electrical distance is obtained from the derived stability criterion. The small perturbation analysis and electromagnetic transient simulation give a demonstration to the analysis.

Stability Analysis of Cohen–Grossberg Type BAM Neural Network with Piecewise Constant Argument

This paper introduces the stability problems of Cohen–Grossberg type BAM neural network (BAMCGNN) with piecewise constant argument (PCA). By employing the homeomorphism theory, sufficient conditions for the existence and uniqueness of the equilibrium point are obtained; using inequality technique and Lyapunov method, sufficient stability criteria for BAMCGNN with PCA are presented. Finally, a numerical case shows the significance of the results of this paper.

Semi-global exponential stability of stochastic nonlinear functional sampling systems by emulation approach

In this paper, the semi-global exponential stability is studied for the stochastic nonlinear functional systems by emulation of sampled-data controller. In consideration of the stochastic factor, a novel definition of the right and upper Dini’s derivative of the constructed functional is given. Based on this novel definition, combining with stochastic analysis techniques and Lyapunov method, some sufficient criteria for the semi-global exponential stability of the stochastic nonlinear functional systems by suitably fast sampling are given. As a special case, a class of stochastic nonlinear functional systems with multiple time delays is studied and two coefficient type theorems that lead to the semi-global exponential stability of the sampling system are derived. Finally, a practical application about parallel active suspension systems with time delay and stochastic disturbance is discussed at length and the corresponding numerical example is given to illustrate the feasibility of the theoretical results.

A Small-Signal Stability Criterion for DC Microgrid Based on Extended-Gershgorin Theorem

Recent years have witnessed emerging oscillation stability issues in DC microgrid via power electronic converters. Considering the confidentiality of the parameters and structure of power electronic devices, the impedance method is widely used to study the small signal stability. However, the stability assessment based on traditional impedance model and Gershgorin Theorem have some shortcomings for multiple converters DC microgrid. This may lead to the problem that the stability analysis results are not accurate enough or the criteria cannot be applied. In this article, the system is modeled as a medium and high dimensional negative feedback system. Further, a sufficient stability criterion based on extended Gershgorin Theorem is developed through reshaping the range of eigenvalues estimation for the non-diagonal advantage system. Finally, the validity of the criterion is verified by a 6 converters system. Test results indicate the proposed method has the potential to assess the high-order system stability with low computational complexity. Moreover, its low conservatism as a sufficient criterion is helpful to guide the system design.