Problem Of Stability Analysis Research Articles

Finite Time Stability Analysis and Feedback Control for Takagi–Sugeno Fuzzy Time Delay Fractional-Order Systems

This study treats the problem of Finite Time Stability Analysis (FTSA) and Finite Time Feedback Control (FTFC), using a Linear Matrix Inequalities Approach (LMIA). It specifically focuses on Takagi–Sugeno fuzzy Time Delay Fractional-Order Systems (TDFOS) that include nonlinear perturbations and interval Time Varying Delays (ITVDs). We consider the case of the Caputo Tempered Fractional Derivative (CTFD), which generalizes the Caputo Fractional Derivative (CFD). Two main results are presented: a two-step procedure is provided, followed by a more relaxed single-step procedure. Two examples are presented to show the reduction in conservatism achieved by the proposed methods. The first is a numerical example, while the second involves the FTFC of an inverted pendulum, which exhibits both symmetrical dynamics for small angular displacements and asymmetrical dynamics for larger deviations.

Relaxed conditions for parameterized linear matrix inequality in the form of nested fuzzy summations

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.

Bifurcation analysis and control of an improved continuous traffic model considering weather effect

PurposeHighway traffic systems are complex and variable, and studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable bifurcation points can alleviate traffic congestion from a new perspective. Bifurcation analysis is used to explain the changes in system stability, identify the unstable bifurcation points of the system, and design feedback controllers to realize the control of the unstable bifurcation points of the traffic system. It helps to control the sudden changes in the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.Design/methodology/approachIn this paper, we improve the macroscopic traffic flow model by integrating severe weather factors such as rainfall, snowfall, and dust. We use traveling wave transform to convert it into a traffic flow stability model suitable for branching analysis, thus converting the traffic flow problem into a system stability analysis problem. First, this paper derives the existence conditions of the model Hopf bifurcation and saddle-node bifurcation for the improved macroscopic model, and finds the stability mutation point of the system. Secondly, the connection between the stability mutation points and bifurcation points of the traffic system is analyzed. Finally, for the unstable bifurcation point, a nonlinear system feedback controller is designed using Chebyshev polynomial approximation and stochastic feedback control method.FindingsThe Hopf bifurcation is delayed and completely eliminated without changing the equilibrium point of the system, thus controlling the abrupt behavior of the traffic system.Originality/valueCurrently there are fewer studies to explain the changes in the stability of the transportation system through bifurcation analysis, in this paper; we design a feedback controller for the unstable bifurcation point of the system to realize the control of the transportation system. It is a new research method that helps to control the sudden change of the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.

Designing asynchronous resilient sampled data controller for nonlinear Markov jump systems via hidden Markov model and quantum genetic algorithm

The article delves into the problem of stochastic stability analysis for nonlinear Markov jump systems (MJSs) with fuzzy asynchronous resilient sampled-data controllers (SDCs) using hidden Markov model (HMM) and quantum genetic algorithms (QGAs). A novel framework using QGA has been developed to obtain the control gain matrices by solving the linear matrix inequality (LMI). A new criterion is proposed to guarantee the stochastic stability of fuzzy nonlinear MJSs, relying on the mode-dependent Lyapunov-Krasovskii functional (LKF) approach. Standard Chua’s circuit has been used to show the reliability and value of the developed results. Also, the Lorentz system has been explored to demonstrate the non-stochastic case.

Robust stability analysis for uncertain systems with time‐varying delay via variable augmentation approach

AbstractThis paper investigates the problem of robust stability analysis for systems with time‐delays and time‐varying structured uncertainties. The variable augmentation approach and the free‐matrix‐based inequality are employed to retain the linear property of the estimation of the derivative of the Lyapunov–Krasovskii functionals. Moreover, with the use of the variable augmentation approach related to the time‐varying structured uncertainties, the time‐varying S‐Procedure combined with the time‐varying delay and its derivative is employed. As a result, less‐conservative robust stability conditions are derived. In addition, the merits of the augmentation of the time‐varying structured uncertainties over the traditional methods are theoretically demonstrated. Finally, two numerical examples are given to verify the benefits of the proposed methods.

STABILITY AND BOUNDEDNESS ANALYSIS OF A STATE–DEPENDENT DIFFERENTIAL EQUATIONS FOR A SYSTEM OF TWO COUPLED CIRCUITS

Two coupled circuits are extensively used in radio electronics and communication. The problem of stability analysis of state variables describing system of two coupled circuits is very critical as unstable circuit causes damage to electrical systems. Analysis of stability and boundedness behavior of the state variables characterizing system of two coupled circuits is carried out using the Lyapunov's second method. We provide in simple form, less restrictive conditions that are implementable at the development stage and which ensure the stability and boundedness of the state variables describing system considered. For illustration, the behaviours of the system of two coupled circuits with response and its bounded output are shown.

Sampled-data stabilization for networked control systems under deception attack and the transmission delay

For the stability analysis and stabilization synthesis problems, this paper considers networked control systems (NCSs) with the transmission delay and the deception attack under aperiodic samplings, where the deception attack and its activation function are represented as a sector bound function and a random variable with Bernoulli distribution, respectively. This paper proposes the stability and stabilization criteria for the NCSs by constructing Lyapunov–Krasovskii (L–K) functionals with continuous functionals and looped-functionals. Compared with the literature, the proposed continuous functionals take into account the mixed delay including the transmission delay and the maximum allowable sampling interval, as well as the augmented vector and integral terms. Also, the proposed looped-functionals construct two augmented vectors with integral vectors that are zeros at t=tk and t=tk+1, respectively. By utilizing these two augmented vectors, the looped-functionals fully utilize the sampling patterns compared with the literature. Based on the proposed L–K functionals, this paper derives not only the stability criterion for the NCSs with the transmission delay, but also the stabilization criterion for the NCSs with the transmission delay and the deception attack in terms of linear matrix inequalities (LMIs), respectively. Numerical example demonstrates the validity of the proposed approach.

Global stability analysis and optimal control problem arise from tuberculosis transmission model with monitored treatment

Global stability analysis and optimal control problem arise from tuberculosis transmission model with monitored treatment

Nonfragile containment control of nonlinear multi‐agent systems via a disturbance observer‐based approach

AbstractIn this article, we consider the nonfragile containment control problem of nonlinear multi‐agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer‐based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with nonfragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques.

THE EFFECT OF VISCOUS DISSIPATION ON THE ONSET OF INSTABILITY OF MAGNETO HYDRODYNAMIC FLOW IN A POROUS MEDIUM

The study of flow of fluid with its motion was study in the nineteenth century by Maurice Couette which was as a result of two parallel plates in which the movement are relative, such that the surfaces is moving laterally. The plates with varying radii, could be flat, parallel or two concentric which is generally referred to as plane Couette. Characteristics of fluid at rest or in motion may undergo changes and become unstable. The critical value or range of the parameters of flow which will give rise to instabilities is one of the problems of stability analysis. The stability of fluid motion may be tested by perturbing the fluid with a small sinusoidal disturbances on the parameter. In plane Couette where moving plates drive the flow and plane Poiseuille flow where a pressure gradient drives the flow, in the situation of weak flow and strong distortional elasticity, an asymptotic analysis will yields closed - form steady solutions with identical wall conditions which will focus on simulations will expose the effects due to wall anchoring conflicts and illustrate the induced morphology of the orientation distribution, stored viscoelastic stresses and non - Newtonian flow.

Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications

Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a so-called symplectic Stiefel manifold, Riemannian optimization is preferred, because one can borrow ideas from unconstrained optimization methods after preparing necessary geometric tools. Retraction is arguably the most important one which decides the way iterates are updated given a search direction. Two retractions have been constructed so far: one relies on the Cayley transform and the other is designed using quasi-geodesic curves. In this paper, we propose a new retraction which is based on an SR matrix decomposition. We prove that its domain contains the open unit ball which is essential in proving the global convergence of the associated gradient-based optimization algorithm. Moreover, we consider three applications—symplectic target matrix problem, symplectic eigenvalue computation, and symplectic model reduction of Hamiltonian systems—with various examples. The extensive numerical comparisons reveal the strengths of the proposed optimization algorithm.

Optics-based metaheuristic approach to assess critical failure surfaces in both circular and non-circular failure modes for slope stability analysis

In many construction projects, a proactive slope stability evaluation is a prerequisite. Although many deterministic or non-deterministic approaches have been commonly used, metaheuristic approaches have resulted in high precision and significant outcomes for slope stability analysis problems. The current work focuses on the reliable assessment of critical failure surfaces associated with the least factor of safety value in both homogeneous and non-homogeneous slopes using a new simplified meta-heuristic approach called optics-inspired optimization (OIO). The algorithm utilizes six different LEM methods as a fitness function for deriving the factor of safety. Experimental analysis over three benchmark studies has been performed to demonstrate the algorithm's robustness and effectiveness. The implementation found more robust results as compared to previous studies. Meanwhile, the algorithm's statistical implication is conducted using the ANOVA test, which inferred better outcomes. With this interpretation, the approach claims to be suitable and efficient for slope stability analysis.

Application of linear ordinary differential equations to the stability control of long time lag networks

Abstract Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (< 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T * = 0.52, T 1 = 0.71 and T 2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.

Formula omitted] stability analysis of neural networks with multiple time-varying delays

This paper studies the problem of Lp stability analysis of neural networks (NNs) with multiple time-varying delays. The delays can be bounded or unbounded. Firstly, a new method based on system solutions is proposed, from which new Lp stability criteria are obtained. On the one hand, the method is convenient to deal with the cases of multiple delays. On the other hand, this method does not need to establish any Lyapunov–Krasovskii functional (LKF), which can greatly reduce the amount of calculations. The obtained Lp stability conditions are simpler, and can be checked by standard software tools. The advantages of the obtained Lp stability conditions are demonstrated with representative numerical examples. It is worth emphasizing that this article is the first time to analyze the Lp stability of NNs with multiple time-varying delays.

Sliding mode control for the discrete cyber‐physical systems under aperiodic denial‐of‐service attacks

AbstractIn this work, the problems of stability analysis and sliding mode control (SMC) for discrete‐time cyber‐physical systems (CPSs) under denial‐of‐service (DoS) attacks are investigated. Firstly, the model of aperiodic DoS attacks is established by introducing the constraints on the upper bound of the attack interval and the lower bound of the non‐attack interval. Next, by utilizing the SMC and switching strategies, the input‐to‐state stability (ISS) of the CPSs can be guaranteed in terms of the upper and lower bounds restrictions. Then, the sliding mode control law is designed for the considered CPSs. Finally, one example is given to illustrate the applicability of our proposed theoretical result.

Adaptive event-triggered synchronization of neural networks under stochastic cyber-attacks with application to Chua’s circuit

This paper focuses on the synchronization control problem for neural networks (NNs) subject to stochastic cyber-attacks. Firstly, an adaptive event-triggered scheme (AETS) is adopted to improve the utilization rate of network resources, and an output feedback controller is constructed for improving the performance of the system subject to the conventional deception attack and accumulated dynamic cyber-attack. Secondly, the synchronization problem of master–slave NNs is transformed into the stability analysis problem of the synchronization error system. Thirdly, by constructing a customized Lyapunov–Krasovskii functional (LKF), the adaptive event-triggered output feedback controller is designed to ensure the synchronization error system is asymptotically stable with a given H∞ performance index. Lastly, in the simulation part, two examples, including Chua’s circuit, illustrate the feasibility and universality of the related technologies in this paper.

STABILIZATION OF DISCRETE-TIME SYSTEMS WITH STATE-DELAYS AND SATURATING CONTROL INPUTS

Context. The presence of time delays occurs in many complex dynamical systems, particularly in the areas of modern communication and information technologies, such as the problem of stabilizing networked control systems and high-speed communication networks. In many cases, time-delays lead to a decrease in the efficiency of such systems and even to the loss of stability. In the last decade, many interesting solutions using the Lyapunov-Krasovskii functional have been proposed for stability analysis and synthesis of a stabilizing regulator for discrete-time dynamic systems with unknown but bounded state-delays. The presence of nonlinear constraints on the amplitude of controls such as saturation further complicates this problem and requires the development of new approaches and methods.
 Objective. The purpose of this study is to develop a procedure for calculating the control gain matrix of state feedback that ensures the asymptotic stability of the analyzed system, as well as a procedure for calculating the maximum permissible value of the state-delay under which the stability of the closed-loop system can be ensured for a given set of admissible initial conditions.
 Method. The paper uses the method of descriptor transformation of the model of a closed-loop system and extends the invariant ellipsoids method to systems with unknown but bounded state-delays. The application of the Lyapunov-Krasovskii functional and the technique of linear matrix inequalities made it possible to reduce the problem of calculating the control gain matrix to the problem of semi-definite programming, which can be solved numerically. An iterative algorithm for solving the bilinear matrix inequality is proposed for calculating the maximum permissible value of the time-delay.
 Results. The results of numerical modeling confirm the effectiveness of the proposed approach in the problems of stabilizing discrete-time systems under the conditions of state-delays and nonlinear constraints on controls, which allows to recommend the proposed method for practical use for the problem of stability analysis and synthesis of stabilizing regulator, as well as for calculating the maximum permissible value of time-delay.
 Conclusions. An approach is proposed that allows extending the invariant ellipsoids method to discrete-time dynamic systems with unknown but bounded state-delays for solving the problem of system stabilization using static state feedback based on the application of the Lyapunov-Krasovskii functional. The results of numerical modeling confirm the effectiveness of the proposed approach in the presence of the saturation type nonlinear constraints on the control signals.

The observed mode dependent controller design problem for a class of continuous‐time hidden semi‐Markov jump systems

SummaryThis paper studies the stability analysis and stabilization synthesis problems for a class of continuous‐time jump systems with hidden system modes. To precisely model the switching signals of the considered systems, a novel definition of continuous‐time hidden semi‐Markov process is proposed based on the notions of emission probability and time varying dual‐index transition rate. By virtue of such definition, a dual‐index Lyapunov function is utilized to derive the sufficient stability conditions of the considered systems. By adopting a technology that can decouple the nonlinear terms in the above conditions, the numerically testable existence conditions of the controller for the resulting stabilizing systems are presented. An example is given to illustrate the effectiveness of our results.

Stability Analysis of Cyber-physical System Under Transmission Delay

With the intimate integration of power grids and cyber networks, limited bandwidth and packet delay have a rapidly expanding negative impact on power system performance. The presented multi-area interconnected power system consists of four areas, each including thermal and hydro-generation plants. This paper investigates the stability analysis problem for cyber-physical systems with a round-robin communication protocol under mixed cyberattacks and load changes. The objective is to stabilize a multi-area interconnected power system (MAIPS) using a static feedback controller while minimizing the defined performance function. Then, the stability of the MAIPS is characterized when the system is subjected to a transmission delay while considering predetermined limits for the duration and the frequency of the delay. Our findings indicate that time delays can influence system stability and that choosing an appropriate sampling interval is necessary to ensure the stability of the system. Finally, an illustrative example of three areas of interconnected power systems with several scenarios is presented to verify the effectiveness of the proposed method.

Data-Driven $\mathcal {L}_{2}$-Stability Analysis for Dynamic Event-Triggered Networked Control Systems: A Hybrid System Approach

This paper addresses the problem of data-driven control and stability analysis for networked control systems (NCSs). The systems considered in this paper are assumed to be linear with unknown system matrices and bounded external disturbance. Firstly, a static state-feedback controller is derived directly from noisy data in the absence of network. Secondly, the NCSs including a dynamic event-triggering mechanism (DETM) and time-varying transmission delays are modeled as a hybrid system. Then the <inline-formula><tex-math notation="LaTeX">$\mathcal {L}_{2}$</tex-math></inline-formula>-stability conditions for the hybrid system are established by using the Lyapunov stability approach. Thirdly, by combining the model-based conditions and the parametric representation of the unknown system matrices, data-based stability conditions are derived. Based on the methods proposed in this paper, many well-established model-based theorems can be readily applied to the unknown linear systems. Finally, the proposed theories are verified on a turbofan engine hardware-in-the-loop (HIL) simulation platform.