Problem Of Stability Analysis Research Articles

Stability Analysis of Delayed Recurrent Neural Networks via a Quadratic Matrix Convex Combination Approach.

This brief addresses the stability analysis problem of a class of delayed recurrent neural networks (DRNNs). In previously published studies, the slope information of activation function (SIAF) is just reflected in three slope information matrices, i.e., the upper and lower boundary matrices and the maximum norm matrix. In practice, there are 2n possible combination cases on the slope information matrices. To exploit more information about SIAF, first, an activation function separation method is proposed to derive n slope-information-based uncertainties (SIBUs) containing SIAF; second, a quadratic matrix convex combination approach is proposed to dispose n SIBUs using 2n combination slope information matrices. Third, a stability criterion with less conservatism is established based on the proposed approach. Finally, two simulation examples are used to testify the validity of theoretical results.

The novel impulsive switching conditions for stability of impulsive switched stochastic systems

This paper studies the problems of stability analysis and stabilisation synthesis for a class of impulsive switched stochastic systems. By constructing a novel impulsive switching condition, the sufficient conditions of globally asymptotic stability in probability and stochastic input-to-state stability for the considered systems are presented. Furthermore, the stabilising controller design method can be presented for the corresponding closed-loop systems. Two examples are given to illustrate the effectiveness of the obtained results.

Extended affine bessel summation inequalities: Applications to stability analysis of linear discrete-time systems with time-varying delays

This paper concerns the stability analysis problems of linear discrete-time systems with time-varying delays. For developing less conservative stability criteria obtained with the Lyapunov-Krsoavkii approach, numerous Lyapunov-Krasovskii functional (LKF) have been constructed by utilizing various summation quadratic functions. Thus, summation inequalities have been essential methods to develop convex stability criteria which guarantee the negative forward difference of LKFs. To further reduce the conservatism of stability criteria, this paper proposes extended affine Bessel summation inequalities. The proposed summation inequalities provide affine upper bounds of an extended summation quadratic function that contains a systems state variable, its forward difference, and their correlated terms. Further, this paper provides notes on the correlation among several summation inequalities including the proposed ones. These notes also prove that an increase in the degree of the developed affine Bessel summation inequalities only reduces conservatism. Two numerical examples effectively demonstrate the reduction of the conservatism due to the proposed summation inequalities in terms of stability regions which are expressed as delay bounds.

Consensus control of semi‐Markov jump topology multiple direct‐drive motion system

AbstractRandom jump of network communication topology challenges the tracking accuracy of linear switched reluctance motor (LSRM) system. This paper studies the pilot‐following consensus control of the multiple direct‐drive motion system (MDDMS) with semi‐Markov jump topology. The mathematical model of LSRM is constructed and the multi‐phase excitation strategy is studied. The directed graph is used to model the information transmission among the leaders and follower, and a new mechanism consensus based on previous states is provided. A consensus system based on semi‐Markov jump topology is constructed and the problem of consensus is shifted into a problem of stability analysis. A sufficient condition for consensus problem is obtained by using semi‐Markov switching system theory and graph theory. The MDDMS achieves consensus in the form of exponential convergence under the designed consensus controller. Several groups of simulation results verify the effectiveness of the proposed consensus control method.

Robust stability of uncertain stochastic switched inertial neural networks with time‐varying delay using state‐dependent switching law

In this paper, the problem of robust stability analysis for a type of uncertain stochastic switched inertial neural networks (SSINNs) with time‐varying delay is investigated. First, the original second‐order system is converted into first‐order differential equations using the variable transformation method. Next, some sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained using Lyapunov‐Krasovskii functional (LKF), state‐dependent switching (SDS) method, and Jensen's integral inequality for estimating integral inequalities so that the augmented system is robust, global, and asymptotically stable in the mean square for the uncertain SSINNs with time‐varying delay. It is shown that the stability of the above considered system composed of all unstable subsystems can be achieved by using the SDS law. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed SDS law.

A Linear Time-Varying Inequality Approach for Prescribed Time Stability and Stabilization.

This article studies the problem of finite-time, fixed-time, and prescribed-time stability analysis and stabilization. First, a linear time-varying (LTV) inequality-based approach is introduced for prescribed-time stability analysis. Then, it is shown that the existing nonlinear Lyapunov inequalities-based finite- and fixed-time stability criteria can be recast into the unified framework of the LTV inequality-based approach for prescribed-time stability. Finally, the unified LTV inequality-based approach is used to solve the global prescribed-time stabilization problem of the attitude control system of a rigid spacecraft with disturbance, and a bounded nonlinear time-varying controller is proposed via back stepping. Numerical simulations are presented to show the effectiveness of the proposed methods.

Stability Analysis of Continuous-Time Recurrent Neural Networks by IQC with Copositive Multipliers

This paper addresses the stability analysis problem of recurrent neural networks (RNNs) with activation functions being rectified linear units (ReLUs). In particular, we focus on the linear nonegative properties of the input-output signals of ReLUs. To capture these linear properties within the framework of integral quadratic constraint (IQC), we introduce a copositive multiplier constructed from a copositive matrix. This enables us to capture the linear input-output properties of ReLUs in quadratic form. By using the copositive multipliers in additon to existing multipliers, we can reduce the conservatism of the IQC-based stability analysis for RNNs. We also show that the proposed IQC-based stability condition with copositive multipliers can be viewed as an extension of a recently proposed scaled small-gain stability condition based on the L2+ induced norm.

Finite-time stability analysis of switched systems with actuator saturation based on event-triggered mechanism

Under the event-triggered scheme, this note focuses on the problem of finite-time stability analysis of the switched system with controller failure and external interference. Firstly, in order to save network communication resources, the mixed event-triggered condition is considered. This mechanism can not only avoid Zeno phenomenon, but also use the sampled information more effectively. In addition, the saturation characteristics of the actuator are fully considered, which can further reduce the number of triggers. According to different event-triggered conditions, an algorithm is proposed to estimate the attraction domain. Then, through the Lyapunov-Krasovskii functional approach and average dwell time technology, the closed-loop switched system is analyzed. The determination condition of finite-time stability is obtained. To illustrate the advantages of our established results, a numerical example is finally given. In addition to saving communication resources, the system stability is guaranteed. The advantages of the proposed method can be verified by simulation.

Robust Convergence Analysis of Moving-Horizon Estimator for LPV Discrete-Time Systems*

This paper deals with the problem of robust stability analysis of Moving Horizon Estimator (MHE) for Linear Parameter Varying (LPV) systems. The main contribution of the paper lies in the introduction of novel stability analysis tools guaranteeing exponential robust convergence of the MHE under only the incremental Exponential Input-Output-to-State Stability (i-EIOSS) assumption. Indeed, the i-EIOSS property characterizes the detectability of a system, which is a less conservative assumption compared to the observability condition.

Robust stability and fuzzy controller synthesis for a class of hybrid re-entrant manufacturing systems

This paper addresses the problem of stability analysis and state feedback fuzzy control design for multi-line re-entrant manufacturing systems (RMSs) with impulse-type state jumps. Under the impulse effect, the RMS is modeled as a hyperbolic impulsive partial differential equation (IPDE) that possesses hybrid characteristics. Then, a matrix inequality condition depending on the discrete dynamic information is presented to deal with the jump behavior of the IPDE at impulse instants. Moreover, a robust fuzzy controller based on the parallel distributed compensation scheme is derived to render the RMS to a desired producing mode with steady feeding and output rates. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed robust fuzzy controller.

A linear matrix inequality–based approach for estimating upper bound of settling time

In this article, an upper bound on the settling time is provided for exponentially stable systems by the Lyapunov theory. In order to obtain a more accurate estimate on the upper bound of settling time, an optimization problem with a nonlinear objective function needs to be solved. Since this is a complex problem, a linear matrix inequality–based algorithm is proposed to solve it. Then, we address the stability analysis problem of linear systems with the aim to derive the upper bound on the settling time. This problem is extended to design a static feedback controller for linear systems under input saturation. By solving the optimization problem, the upper bound of the settling time for the closed-loop system is minimized. Finally, the validity and effectiveness of the proposed method are verified by the simulation results and comparisons.

Obtaining initial data for forecast engineering geological model construction

Objective and relevance. Technologies in mining and geology are intensely developing making the present research particularly relevant. The research considers the problems of obtaining reliable and high-quality data on the degree and nature of rock mass fracturing in a solid mineral deposit. These are fundamental data required to construct a forecast engineering geological model of a deposit. The engineering geological model is usually based on a structural geological model with the addition of various geomechanical parameters used in generally accepted international classifications for rock stability analysis, in particular, RMR (Bieniawski), MRMR (Laubscher), and Q-system (Barton). Methods of research. The authors describe the procedure for obtaining classification geomechanical parameters of a rock mass according to the data from oriented and non-oriented core drilling of special engineering geological (geomechanical) boreholes. Research results. The main factors and conditions for reliable data acquisition are given. Among the most important ones are: economic feasibility and validity of geomechanical boreholes drilling as well as their number; features of the geological and structural composition of a deposit as a condition for borehole location selection; proper organization of the drilling process aimed at obtaining high-quality core material; characteristics of geomechanical description of the core, depending on the rating system of rock mass classification applied. Scope of results. By way of example, deposits with different geological and structural conditions are listed where the described procedure was applied. High-quality and reliable information about the structural and tectonic features of the rock mass allows to create and fill the engineering geological model with data and solve the problems of stability analysis for almost any area of the future mine working.

Bifurcation analysis of a new stochastic traffic flow model

Abstract The stochastic function describing the stochastic behavior of traffic flow in the process of acceleration or deceleration can better capture the stochastic characteristics of traffic flow. Based on this, we introduce the stochastic function into a high-order viscous continuous traffic flow model and propose a stochastic traffic flow model. Furthermore, we performed the bifurcation analysis of traffic flow system based on the model. Accordingly, the traffic flow problem is transformed into the stability analysis problem of the system, highlighting the unstable traffic characteristics such as congestion. The model can be used to study the nonlinear dynamic behavior of traffic flow. Based on this model, the existence of Hopf bifurcation and the saddle-node bifurcation is theoretically proved. And the type of the Hopf bifurcation is theoretically derived. The model can also be used to study the mutation behavior of system stability at bifurcation point. From the density space-time diagram of the system, we find that the system undergoes a stability mutation when it passes through the bifurcation point, which is consistent with the theoretical analysis results.

Diagonal Stability of Systems With Rank-1 Interconnections and Application to Automatic Generation Control in Power Systems

We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal stability of approximately rank-1 interconnections. The main result is then leveraged as a key step in a larger stability analysis problem arising in power systems control. Specifically, we provide the first theoretical stability analysis of automatic generation control (AGC) in an interconnected nonlinear power system. Our analysis is based on singular perturbation theory, and provides theoretical justification for the conventional wisdom that AGC stabilizes under the typical time-scales of operation. We illustrate how our main analysis results can be leveraged to provide further insight into the tuning and dynamic performance of AGC.

Stability criteria for memristor-based delayed fractional-order Cohen–Grossberg neural networks with uncertainties

This paper investigates the Mittag-Leffler (ML) stability analysis problem of memristor-based fractional-order Cohen–Grossberg neural networks (MFCGNNs) with time delays and uncertainties. The voltage type memristor is taken into consideration. The Cohen–Grossberg neural networks (CGNNs) are described by using fractional-order systems (FOS) unified by memristive circuit elements. Sufficient conditions are derived on the basis of the fractional-order (FO) Lyapunov direct approach, differential inclusion theory, and the Filippov solution. Besides that, the conditions are formed in terms of linear matrix inequalities (LMI), which ensure ML stability for MFCGNNs with time delays. Finally, the validity and efficacy of the obtained theoretical results are demonstrated by appropriate numerical example and simulation results.

Stability analysis and optimization problem fractional of a predator–prey system with Holling II functional response

The Kolmogorov model has been applied to numerous organic and natural issues. We are especially inspired by one of its variations, that is, a Gauss-type hunter prey model that incorporates the allee impact and Holling type-II utilitarian reaction. Rather than utilizing exemplary first request differential conditions to figure the model, fragmentary request differential conditions are used. The presence and uniqueness of a nonnegative arrangement just as the conditions for the presence of balance focuses are given. We then, at that point, examine the neighborhood strength of the three sorts of harmony focuses by utilizing the linearization strategy. This paper manages an ideal control issue of a hunter prey framework with a Holling II useful reaction. The model viable joins an asylum ensuring [Formula: see text] of the prey and leaves ux of the prey accessible to the hunter, where [Formula: see text]. By using Pontryagin’s Most extreme Standard for partial, we concentrate on the ideal control issue viewing u as a control work.

Order‐dependent and delay‐dependent conditions for stability and stabilization of fractional‐order time‐varying delay systems using small gain theorem

AbstractIn this paper, the stability and stabilization problems for fractional‐order time‐varying delay systems are investigated. Firstly, by casting the stability problem as one of robust stability analysis problems and utilizing the small gain theorem, an order‐dependent and delay‐dependent stability condition for fractional‐order time‐varying delay systems is developed. Taking advantage of the information of order and delay, the stability condition is less conservative than the existing results. Then, state feedback controllers that stabilize fractional‐order time‐varying delay systems are developed. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, numerical examples are provided to illustrate that the proposed criteria are valid and less conservative than the existing ones.

Strong delay-independent stability analysis of neutral delay systems with commensurate delays

This paper considers the strong delay-independent stability analysis problem of neutral delay systems with commensurate delays. Different from the existing method with the considered original system being first transformed into a high dimensional neutral system, our proposed method directly deals with the original system. First, a new family of linear matrix inequalities, indexed by a positive integer k, is derived to assess the strong delay-independent stability. It is shown that the proposed condition possesses a lower computational burden than the existing results. Then, a time-domain interpretation of the proposed condition is given in terms of a quadratic integral Lyapunov functional. Finally, based on the fact that the established condition involves matrices that are linear functions of the coefficients of the neutral delay systems, the proposed condition is further used to solve the robust strong delay-independent stability analysis problem of neutral delay systems with norm bounded uncertainty. Numerical examples are employed to illustrate the effectiveness of the proposed results.

Quantized-communication-based neural network control for formation tracking of networked multiple unmanned surface vehicles without velocity information

This paper proposes a quantized communication-based output-feedback control strategy for formation tracking of networked unmanned surface vehicles (USVs) with uncertainty. Under limited network communication, it is assumed that each USV measures only the position and orientation information. In particular, this information is quantized and transmitted to USVs connected to a band-limited directed network. The primary contributions of this study are to derive distributed learning laws for neural networks using discontinuous signals and to analyze the stability of the neural network-based output-feedback control system designed in a quantized communication environment. A neural network-based local observer is developed to estimate the velocity information of each USV with model uncertainty and external disturbance. Then, a neural network-based output-feedback control design strategy using distributed and quantized postures is presented to accomplish the desired formation of networked USVs with uncertainty and underactuation. The distributed learning laws of neural networks are derived using neighbors’ quantized signals. The auxiliary signal and approach angle are employed to solve the underactuation and stability analysis problems. Despite the discontinuity of quantized signals, it is proven that all errors in the closed-loop system are bounded and can be made arbitrarily small. Finally, simulation results are given to verify the theoretical results of the proposed control system.

Delay-Dependent Stability for Load Frequency Control System via Linear Operator Inequality

The stability analysis problem is considered for multiarea load frequency control (LFC) systems with electric vehicles (EVs) and time delays. The novel linear operator inequality approach is proposed and a less conservative delay-dependent stability condition is achieved. First, the model of the multiarea LFC system with EVs and delays is expressed by the partial integral equation (PIE) at the first time. Then, a complete quadratic Lyapunov-Krasovskii functional is built in the form of an inner product of the linear partial integral (PI) operator. The novel stability criteria with less conservatism are proposed in the form of linear operator inequality. Moreover, the relationships between the delay margins and the controller parameters are shown. Finally, the simulations are conducted on both one-area and two-area LFC systems to show the effectiveness of the proposed approach.