Conditions For Stability Of Systems Research Articles

Reachable set estimation and stochastic sampled-data exponential synchronization of Markovian jump neural networks with time-varying delays

In this paper, the stochastic sampled-data exponential synchronization problem for Markovian jump neural networks (MJNNs) with time-varying delays and the reachable set estimation (RSE) problem for MJNNs subjected to external disturbances are investigated. Firstly, assuming that two sampled-data periods satisfy Bernoulli distribution, and introducing two stochastic variables to represent the unknown input delay and the sampled-data period respectively, the mode-dependent two-sided loop-based Lyapunov functional (TSLBLF) is constructed, and the conditions for the mean square exponential stability of the error system are derived. Furthermore, a mode-dependent stochastic sampled-data controller is designed. Secondly, by analyzing the unit-energy bounded disturbance of MJNNs, a sufficient condition is proved that all states of MJNNs are confined to an ellipsoid under zero initial condition. In order to make the target ellipsoid contain the reachable set of the system, a stochastic sampled-data controller with RSE is designed. Eventually, two numerical examples and an analog resistor–capacitor network circuit are provided to show that the textual approach can obtain a larger sampled-data period than the existing approach.

A spatiotemporal fuzzy control approach for complex distributed parameter system with application to thermal processes

Many industrial processes belong to distributed parameter systems (DPSs) with unknown spatiotemporal dynamics and complex boundary conditions. However, attentions to both temporal and spatial dynamics in the control law are less paid in the existing control methods, which often makes them challenging to achieve accurate control. Here, a spatiotemporal fuzzy control approach with consideration of both temporal and spatial dynamics is proposed for unknown and complex DPSs. First, a spatiotemporal fuzzy model is developed to reconstruct dynamics of nonlinear DPS. Since it constructs a two-layer fuzzy rules (i.e., temporal fuzzy rule and spatial fuzzy rule) to consider both the nonlinear dynamics on time and the nonlinear energy transfer on space, it can effectively achieve the model of DPSs. On this basis, a spatiotemporal fuzzy controller is developed according to the developed two-layer fuzzy rules, which means that this derived control law considers both temporal and spatial dynamics. Then, a two-step solution method is designed for the spatiotemporal control law. Stability conditions of the control system are rigorously deduced by transforming the solving process to a series of linear matrix inequalities (LMIs). The stability and effect of the proposed spatiotemporal control strategy are demonstrated by mathematical proof and case studies. Comparison results demonstrate that the proposed method has better control performance (relative errors and mean absolute percentage errors are bounded in 4%).

Robust control strategy for networked vehicle system with fake data injection attack

This article investigates the safety control problem of intelligent networked vehicle and utilizes the sliding-mode control to solve the system with time delay, system disturbance, and parameter uncertainty. First, the modeling of automobile system is introduced. What’s more, time delay, parameter uncertainty, disturbance, and attack are added to the original model. Then, designed an integral sliding-mode surface and given the sufficient conditions for system stability using linear matrix inequalities. Furthermore, the controller is designed according to the slide approach rate, and it is proved that the designed controller can make the system state reach the sliding surface in finite time. Finally, the simulation is used to verify the effectiveness of the arithmetic.

Asymptotic Properties of a Class of Systems with Linear Delay

Sufficient conditions for the asymptotic stability of linear systems of differential equations with linear delay are obtained. On the basis of these conditions, some systems of linear differential equations are studied, and one of them is stabilized on an infinite time interval.

Interconnected Systems Modelling in Food Industry: General Solution Scheme and Stability Conditions for Linear Time-Invariant Systems

The problem of simulating complex systems, such as production lines, industrial plants, food processing, etc., today represents an opportunity that brings with it the great advantage of limiting design costs. However, nowadays the designer, after defining and implementing the mathematical models of the studied process, may need to rebuild the whole simulation framework because he needs to modify the model of even just one subsystem. It is for this reason that in this paper, a new framework for the use of Individual Subsystem Models (ISM) for the modelling and simulation of interconnected systems has been studied and implemented. Furthermore, the study of the state of the art has revealed the lack of efficient and sufficiently general numerical algorithms, but, at the same time, it is simple to use to solve the algebraic-differential equations deriving from the ISM simulation. The proposed new approach follows the paradigm of co-simulation methods, including graph theory methods, to solve the general ISM simply and efficiently. In this approach, each subsystem is required to have its own representation independently of the other subsystems. In this way, it is always possible to replace any subsystem whenever an updated representation becomes available, making maintenance and evolution of the entire ISM flexible. Our framework calls each subsystem separately in an optimal (suboptimal) order based on the structure of the graph. Each calculated output is transferred to the input of the next subsystem in the chosen. The general procedure has been validated in the context of Linear and Time-Invariant ISMs: in these hypotheses, the stability conditions have been calculated and numerical tests have been performed which show the effectiveness of the proposed approach.

A chaos control strategy for the fractional 3D Lotka–Volterra like attractor

In this paper, we have considered a three-dimensional Lotka–Volterra attractor in the frame of the Caputo fractional derivative to examine its dynamics. The theoretical concepts like existence and uniqueness and boundedness of the solution are analyzed. To regulate the chaos in this fractional-order system, we have developed a sliding mode controller and conditions for global stability of the controlled system with and without uncertainties and outside disruptions are derived. The ability of the designed controller is examined in terms of both commensurate and non-commensurate fractional order derivatives for all the aspects. The Lyapunov exponent is the novelty of this paper which is used to illustrate the behavior of the chaos and demonstrate the dissipativeness of the considered chaotic system. We have examined the effect of fractional order derivatives in this system. With the help of numerical simulations, the theoretical claims regarding the impact of the controller on the system are established.

Fixed-Time and Predefined-Time Stability of Impulsive Systems

Dear Editor, This letter establishes several criteria for fixed-time stability and predefined-time stability of impulsive systems. First, sufficient conditions for fixed-time stability of impulsive systems are presented to treat the destabilizing impulses and hybrid impulses involving multiple jump maps by fixed-time control without linear feedback regulation. It determines the robustness of nonlinear systems against impulsive disturbance which has destabilizing and hybrid effect to dynamics. Then, the predefined-time stability of impulsive systems is ensured under the requirement that the hybrid impulses have stabilizing accumulative effect. Finally, the validity of theoretical results is verified by the allocation of mobile agents on a segment via fixed-time control with impulsive regulation.

Practical consensus for heterogeneous multi-agent systems with gain fluctuations via resilient sampled-data control

This study proposes a sampled-data-based practical consensus control method for heterogeneous multi-agent systems with gain fluctuations. First, the heterogeneous multi-agent system is formulated together with randomly occurring nonlinear dynamics. Second, unlike the existing studies, a more general retarded sampled-data control approach is designed, which involves the gain fluctuations along with the actual sampling pattern and constant time delay, to achieve the practical consensus of the considered system. By utilizing the aperiodic sampling information, and looped functional approach, a Wirtinger’s inequality-based discontinuous Lyapunov-Krasovskii functional is constructed to derive the delay-dependent stability condition of the closed-loop system in the form of linear matrix inequality. Finally, numerical simulation is presented to illustrate the derived theoretical results.

Disturbance Rejection and Control System Design Based on an Improved Equivalent-Input-Disturbance Approach

This article presents an improved equivalent-input-disturbance (EID) approach to actively rejecting exogenous disturbances for a plant. A control system based on the approach includes a new EID estimator constructed by embedding integrals to the conventional EID estimator. These integrals enable the estimator to improve the disturbance-estimation precision without amplifying the effect of measurement noise. Stability conditions of the control system are obtained using separation theorem. The system design ensures that the control system satisfies the stability conditions. Experiments of a rotational control system demonstrate the validity of the approach.

A novel collapse prediction index for voltage stability analysis and contingency ranking in power systems

Voltage instability is a serious phenomenon that can occur in a power system because of critical or stressed conditions. To prevent voltage collapse caused by such instability, accurate voltage collapse prediction is necessary for power system planning and operation. This paper proposes a novel collapse prediction index (NCPI) to assess the voltage stability conditions of the power system and the critical conditions of lines. The effectiveness and applicability of the proposed index are investigated on the IEEE 30-bus and IEEE 118-bus systems and compared with the well-known existing indices (Lmn, FVSI, LQP, NLSI, and VSLI) under several power system operations to validate its practicability and versatility. The study also presents the sensitivity assumptions of existing indices and analyzes their impact on voltage collapse prediction. The application results under intensive case studies prove that the proposed index NCPI adapts to several operating power conditions. The results show the superiority of the proposed index in accurately estimating the maximum load-ability and predicting the critical lines, weak buses, and weak areas in medium and large networks during various power load operations and contingencies. A line interruption or generation unit outage in a power system can also lead to voltage collapse, and this is a contingency in the power system. Line and generation unit outage contingencies are examined to identify the lines and generators that significantly impact system stability in the event of an outage. The contingencies are also ranked to identify the most severe outages that significantly cause voltage collapse because of the outage of line or generator.

Global fractional Halanay inequalities approach to finite-time stability of nonlinear fractional order delay systems

In this paper, we investigate the robust finite time stability of fractional order systems with time varying delay and nonlinear perturbation. We improve the sufficient condition for general fractional delay systems by utilizing the special structure of a singular Gronwall inequality. For stable fractional delay systems, our approach bases on a global Halanay type inequality in differential and integral forms. A sharper delay dependent sufficient condition for robust finite time stability of such systems is formulated in terms of the Mittag-Leffler functions and the delayed size. The connection between the new sufficient condition and the previous results is compared and discussed thoroughly.

A novel hierarchical temperature control method of an electric oven and its experimental evaluation

PurposeOvens are semi-industrial multipurpose equipment that are used to provide a desired temperature for specific chemical processes. Temperature regulation in the presence of different type of disturbances and dealing with nonlinear dynamics with large dead time (up to a few minutes) are some undesirable factors that have to be considered in the controller design procedure of the oven systems. Due to these factors, the classical PID controller tuned using Cohen-Coon or Ziegler–Nichol’s tuning methods often fails to meet satisfactory closed-loop performance.Design/methodology/approachIn this paper, to deal with the limitations on the oven system due to the undesirable factors, a hierarchical automaton-guided form controller has been designed. The proposed controller includes several discrete PI controllers, each of which operates locally in the defined operating regions whose separation idea is specific to this paper. Based on the idea proposed in the separation of regions, the controller’s coefficients tuning rules are extracted prior to any determination. Then, a supervisor controller has assumed the task of switching between local controllers. In the next step, by considering a conceptual model for the oven system and using a candidate Lyapunov function, the stability conditions of closed-loop system are discussed and the necessary conditions for the asymptotic stability are derived. The proposed controller is practically implemented with the help of the Arduino Nano platform.FindingsUsing several experiments, the superiority of the proposed hierarchical controller in terms of performance and energy consumption has been demonstrated.Originality/valueThe proposed hierarchical controller has been implemented practically and an acceptable closed-loop performance has been achieved. To illustrate the efficiency of the proposed method, the closed-loop stability of this method is shown using the Lyapunov theory.

Asymptotic stability for nonlinear time-varying systems on time scales

This paper is concerned with nonlinear time-varying systems on time scales, which can cover not only trivial continuous and discrete dynamical systems, but also some other nontrivial cases. Some less conservative sufficient conditions for asymptotic stability of nonlinear systems are derived. Compared with the traditional stability results, the negative definiteness of the time derivatives of Lyapunov functions is weakened, that is, the time derivatives of related Lyapunov functions in this paper are allowed to be indefinite. Two examples about trivial and nontrivial systems are included to illustrate the effectiveness of the results obtained.

Synchronization of a vibration system excited by two eccentric rotors on different rigid frames

This paper is focused on synchronization of a dynamic model with three rigid frames (RFs) driven by two reverse rotating eccentric rotors (ERs) distributed on different RFs. The differential equations of motion are established based on Lagrange equation. Applying the average method of small parameters, the condition is derived for the vibration system to meet synchronous motion. The stability condition of the vibration system is obtained by using Lyapunov indirect method. To investigate the selected motion characteristic on synchronous state in various frequency regions, theoretical results are discussed with frequency ratio numerically. Coupled motion of the vibration system, phase difference between two ERs, motion phase between RFs, and amplitude–frequency characteristics of RFs are discussed qualitatively to reveal the selected motion characteristic. A series of experiments are done to further illustrate the selected motion characteristic in sub-resonant state and super-resonant state of the vibration system with vertical direction. Finally, the experimental results validate the predication of the theoretical method.

Reset control and ℒ2-gain analysis of piecewise-affine systems

This paper is concerned with reset controller design and L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results.

Effect of Antiviral Therapy for HCV Treatment in the Presence of Hepatocyte Growth Factor

The effect of antiviral therapy during Hepatitis C Virus (HCV) infection is the focus of this study. HCV infection destroys healthy hepatocyte cells in the human liver, causing cirrhosis and hepatocellular carcinoma. We introduce a cell-population model representing the long-term dynamics of HCV infection in response to antiviral drug therapies. The proliferation of existing cells can create hepatocyte cells in the system. Such models are based on the dynamics of susceptible hepatocytes, infected hepatocytes and HCV with interactive dynamics, which can give a complete understanding of the host dynamics of the system in the presence of antiviral drug therapy. Infection-free equilibrium and endemic equilibrium are two equilibrium states in the absence of drugs. The existence and stability conditions for both systems are presented. We also construct an optimal control system to find the optimal control strategy. Numerical results show that the effects of the proliferation rate and infection rate are critical for the changes in the dynamics of the model. The impact of different weight factors on the optimal control problem is analysed through numerical simulation.

Стабілізація дифузних стохастичних динамічних інформаційних систем з урахуванням зовнішніх випадкових збурень

Conditions for optimal stabilization of diffusive stochastic dynamic systems with external disturbances have been obtained. The purpose of this work is to find the stabilization conditions of diffusive stochastic dynamic systems with external random disturbances.
 The research topic is relevant because the results of the work will allow to investigate the stabilization of dynamic stochastic systems of a random structure, which makes it possible in many cases to stabilize an unstable stochastic system when certain conditions are met.

Transmission synchronization of multiple memristor chaotic circuits via single input controller and its application in secure communication

This article mainly studied the transmission synchronization of multiple memristor chaotic circuits by using a single input controller strategy. For transmission synchronization model, the definition of synchronization is established, and based on the stability of minimum phase system, the sufficient conditions of system stability are obtained to ensure that the system error curves of multiple memristor chaotic circuits can maintain asymptotical synchronization. Furthermore, the results of synchronization circuit experiment illustrate that the designed controller works well for the synchronization of multiple memristor chaotic circuits. Finally, the results of secure communication experiment based on transmission synchronization show that the scheme is feasible.

Data-Driven Output-Feedback Control for Unknown Switched Linear Systems

This paper proposes a data-driven control method to stabilize unknown switched linear systems under arbitrary switching. We consider the case where the system state is not measurable and design an output feedback controller only using measured input-output data. First, the system with multiple outputs is transformed into a single-output system with observability preserved. Then, a data-based state-space representation that has the same input-output relationship as the original system is constructed using the input-output data of the single-output system, based on which the data-driven controller is designed. Sufficient conditions for asymptotic stability of the closed-loop system under arbitrary switching are established in terms of linear matrix inequalities (LMIs). Compared with the existing method, the proposed method decreases the dimension of the constructed data-based state-space representation, which may reduce the computational burden of the controller design. The effectiveness of the proposed controller is illustrated by an example.

Provably-Stable Stochastic MPC for a Class of Nonlinear Contractive Systems

We present a model predictive control framework for a class of nonlinear systems affected by additive stochastic disturbances with (possibly) unbounded support. We consider hard input constraints and chance state constraints and we employ the unscented transform method to propagate the disturbances over the nonlinear dynamics in a computationally efficient manner. The main contribution of our work is the establishment of sufficient conditions for stability and recursive feasibility of the closed-loop system, based on the design of a terminal cost and a terminal set. We focus here on a special class of nonlinear systems that exhibit contractive properties in the dynamics. By assuming this property, we propose a novel approach to efficiently compute the terminal conditions without the need of performing any linearization of the dynamics. Finally, we provide an illustrative example to corroborate our theoretical findings.