Robust Exponential Stability Research Articles

Robust Stability Analysis of Switched Neural Networks with Application in Psychological Counseling Evaluation System

In this work, the effectiveness and stability of psychological counseling are evaluated using the switched complex-valued neural networks (SCVNN) model, which includes parameter disturbances, impulsive perturbations, variable and continuously distributed delays in the system state, and impulsive delay. How to analyze and judge the stability of the network simply and effectively is the primary prerequisite for its successful application. Therefore, we explore the dynamic behavior of SCVNN with both variable and distributed delays along with impulsive effect. Initially, the proposed conditions for the existence and uniqueness of equilibrium in SCVNN are presented. Subsequently, employing the inequality technique and impulsive average dwell time approach, sufficient conditions for the robust exponential stability of SCVNN under both arbitrary and restricted switching are obtained. Lastly, the psychological counseling evaluation system (PCES) is established, and a simulation example is used to verify the correctness and effectiveness of the presented findings.

New Criteria for Robust Exponential Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delay via Average Dwell Time Approach and Under Arbitrary Switching Signal

New Criteria for Robust Exponential Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delay via Average Dwell Time Approach and Under Arbitrary Switching Signal

Global Exponential Robust Stability of Generalized Differential Dynamical System With Deviating Argument and Random Disturbance

Global Exponential Robust Stability of Generalized Differential Dynamical System With Deviating Argument and Random Disturbance

Global robust stability of fuzzy cellular neural networks with parameter uncertainties

<abstract><p>The global robust stability of uncertain delayed fuzzy cellular neural networks (UDFCNNs) was analyzed in this paper. The major results of this paper provided some new criteria for the existence and uniqueness of the equilibrium point of UDFCNN. Furthermore, suitable Lyapunov-Krasovskii functionals was designed for obtaining the adequate conditions for the global asymptotic robust stability and global exponential robust stability of UDFCNN. Finally, several numerical examples was provided to verify the validity of the results.</p></abstract>

Global robust exponential stability of interval BAM neural networks with multiple time-varying delays: A direct method based on system solutions

This paper analyzes global robust exponential stability of interval bidirectional associative memory (BAM) neural networks with multiple time-varying delays, proposes a direct method based on system solutions, and gives sufficient conditions under which interval BAM neural networks have a unique and globally robustly exponentially stable equilibrium point. This method not only avoids the difficult to set up any Lyapunov–Krasovskii functional, but also derives simpler global robust exponential stability criteria. Compared with the data from other literature, the robust exponential stability criteria obtained in this paper have been presented to have more merits theoretically and numerically.

Robust exponential stabilization and L2‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

AbstractFor the nonlinear continuous‐time switched system with input saturation under asynchronous switching action, the problem of actuator failure is investigated in the presence of external disturbances. Firstly, a sufficient condition for the robust exponential stabilization of system is obtained by using the minimum dwell‐time method combining the piecewise Lyapunov function method. Secondly, a sufficient condition for the tolerance disturbances of the system is obtained by using the similar approach. Thirdly, the weighted ‐gain is analysed. Then, we maximize the estimation of the domain of attraction for the closed‐loop system by taking the shape of a set into consideration. Furthermore, the fault‐tolerant state feedback controllers are designed, which aim at enlarging the estimation of domain of attraction for the closed‐loop system and obtaining the maximum value of tolerance disturbance and the minimum upper bound on the weighted ‐gain. Last but not least, we give a numerical example to verify the effectiveness of the proposed approach and compare the state responses curve under the action of the fault‐tolerant and the standard controller.

Ternary Implicit Criterion for Robust Exponential Stability of Perturbed Stochastic BAM Systems

This brief presents the sufficient criterion to guarantee the robust exponential stability (RES) of perturbed stochastic nonlinear bidirectional associative memory system with derivative contraction coefficients and piecewise constant arguments (SDPNBAM system). Different from the method of solving multiple transcendental equations, the upper bounds of derivative contraction coefficients, stochastic disturbances and piecewise constant arguments are parsed by the same well-defined ternary transcendental equation and characterized by a feasible geometrical enclosed space, formulating the main ternary implicit criterion. Accordingly, the dynamical interconnection among perturbed ternary variables constrained in the same transcendental equation is formed and to moderate the SDPNBAM system to be stable ultimately. Finally, the numerical simulation shows the effectiveness of main results.

Resilient control of flexible hypersonic vehicles against unmatched distributed faults

This paper studies a robust fault compensation and vibration suppression problem of flexible hypersonic vehicles. The controlled plant is represented by a cascade system composed of a nonlinear Ordinary Differential Equation (ODE) and an Euler-Bernoulli Beam Equation (EBBE), in which the vibration dynamics is coupled with the rigid dynamics and suffers from distributed faults. A state differential transformation is introduced to transfer distributed faults to an EBBE boundary and a longitudinal dynamics is refined by utilizing T-S fuzzy IF-THEN rules. A novel T-S fuzzy based fault-tolerant control algorithm is developed and related stability conditions are established. The robust exponential stability and well-posedness are proved by using the modified C0-semigroup based Lyapunov direct approach. A simulation study on the longitudinal dynamics of flexible hypersonic vehicles effectively verifies the validity of the developed theoretical results.

Stability analysis for singular random impulsive control system: A novel neutral impulsive delay system approach

The paper studies stability analysis for an uncertain singular time varying delay system (USTDS) under random impulsive control (RIC). It also proves the stability results for a singular impulsive time delay system in terms of neutral impulsive time delay system approach. Besides, we derive the new sufficient conditions for stability results like exponential stability (ES) and robust exponential stability (RES) of the proposed system via linear matrix inequality (LMI) by employing the Lyapunov–Krasovskii functional (LKF) approach. In addition, two numerical examples, along with graphical simulations, are provided to illustrate the validity and effectiveness of the proposed results.

On the Study of Robust Exponential Stability of Continuous- and Discrete-Time Systems

A technique for obtaining sufficient conditions for the robust exponential stability of a parametrically uncertain system is proposed. This technique is used to study both continuousand discrete-time parametrically uncertain systems. For a common Lyapunov function we take a positive definite quadratic form that is a Lyapunov function of the system for a specific parameter value and satisfies some constraints on the first derivative (first difference). The application of our technique is illustrated by specific examples.

Robust exponential stability analysis of switched systems under switching boundary mismatch

AbstractSwitching boundary is an integral part of the switched system, but the existing literature on switched systems does not focus on the system under switching boundary mismatch. In this article, the switching boundary mismatch is considered, and the control strategy based on observation algorithm is designed for the state dependent switched system. By implementing the proposed strategy, the system can realize robust exponential stability and track the desired trajectory. Since the switching boundary mismatch is unmeasurable, an observation algorithm is designed. Combining the observation algorithm and iterative learning control law, the new control strategy can be derived. According to the Lyapunov stability theory and mode dependent average dwell time method, the robust exponential stability conditions of the closed‐loop system based on linear matrix inequalities are given. The mode dependent average dwell time of each subsystem can be solved simultaneously. Finally, simulations have been taken to verify the designed strategy can render the closed‐loop system achieve robust exponential stability and can track the desired trajectory.

On the Study of Robust Exponential Stability of Continuous- and Discrete-Time Systems

On the Study of Robust Exponential Stability of Continuous- and Discrete-Time Systems

Effect of Impulses on Robust Exponential Stability of Delayed Quaternion-Valued Neural Networks

Effect of Impulses on Robust Exponential Stability of Delayed Quaternion-Valued Neural Networks

Integral Sliding Mode Control for a Kind of Impulsive Uncertain Reaction-Diffusion Systems

This article discusses the integral sliding mode control problem for a kind of periodically impulsive uncertain reaction-diffusion systems (IURDSs). A novel integral sliding surface containing impulsive effects and reaction-diffusion terms is constructed, such that the impulsive effects for IURDSs can be removed. A novel sliding mode controller with impulsive effects is designed to ensure the reachability of the specified sliding surface in a finite time interval. By means of linear matrix inequalities (LMIs), the robust exponential stability of this kind of IURDSs are derived. Finally, a numerical example is provided to verify the availability of our findings.

Robust exponential stability of discrete-time uncertain impulsive stochastic neural networks with delayed impulses

This paper is devoted to the study of the robust exponential stability (RES) of discrete-time uncertain impulsive stochastic neural networks (DTUISNNs) with delayed impulses. Using Lyapunov function methods and Razumikhin techniques, a number of sufficient conditions for mean square (RES-ms) robust exponential stability are derived. The obtained results show that the hybrid dynamic is RES-ms with regard to lower boundary of impulse interval if the discrete-time stochastic neural networks (DTSNNs) is RES-ms and that the impulsive effects are instable. Conversely, if DTSNNs is not RES-ms, impulsive effects can induce unstable neural networks (NNs) to stabilize again concerning an upper bound of the impulsive interval. The results obtained in this study have a broader scope of application than some previously existing findings. Two numerical examples were presented to verify the availability and advantages of the results.

Robust exponential stabilization of stochastic coupled T‐S fuzzy complex networks subject to state‐dependent impulsive control

AbstractThe problem of robust exponential stabilization for T‐S fuzzy stochastic dynamical networks (T‐S FSDNs) based on the state‐dependent impulsive controller is investigated in the paper. Using B‐equivalence approach, some sufficient conditions are provided such that every solution of considered systems intersects each impulsive surface exactly once. Then, combining with the inequality technique and comparison principle, some meaningful sufficient criteria are obtained to ensure the mean square stability of T‐S fuzzy stochastic dynamical networks. Compared to related results, the results obtained in the paper are low conservatism and easy to verify. Finally, two numerical simulations based on Rssler's system and Lorenz system show the effectiveness of the obtained theoretical results.

Robust Exponential Stability and Invariance Guarantees with General Dynamic O'Shea-Zames-Falb Multipliers

We propose novel time-domain dynamic integral quadratic constraints with a terminal cost for exponentially weighted slope-restricted gradients of not necessarily convex functions. This extends recent results for sub-differentials of convex function and their link to so-called O'Shea-Zames-Falb multipliers. The benefit of merging time-domain and frequency-domain techniques is demonstrated for linear saturated systems.

Robust Moving-Horizon Estimation for Quasi-LPV Discrete-Time Systems*

This paper deals with moving horizon estimation for a class of quasi-LPV systems. Under both observability condition and incremental exponential input output-to-state stability (i-EIOSS) assumption, novel stability conditions of the moving horizon estimator (MHE) are proposed. Such conditions guarantee exponential robust stability of the MHE based on a particular prediction step that is independent of the dynamic of the system. An application to vehicle motion estimation, using the kinematic model, is provided to show the validity and effectiveness of the proposed method, and to support the theoretical results.

Network‐based robust exponential fuzzy control for uncertain systems

This article studies the robust exponential stability and Takagi–Sugeno (T–S) fuzzy control synthesis for networked control systems via performance. The main aim of this paper is to design fuzzy controllers with less conservative results. Novel weighted integral inequalities (WIIs) are proposed based on Wirtinger's integral inequalities. The T–S fuzzy approach expresses nonlinear systems as linear submodels with IF–THEN rules for deriving the stability conditions. Then, by constructing a suitable Lyapunov–Krasovskii functional (LKF) and applying new WIIs, improved exponential stability and stabilization criteria are established in the form of linear matrix inequalities (LMIs). Three examples are provided to demonstrate the advantages and usefulness of the proposed novel method. Two are application‐oriented examples, such as the variable speed wind turbine (VSWT) system and nonlinear mass‐spring (NMS) system.

Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

AbstractFor nonlinear uncertain switched systems, the problem of how to overcome the controller vulnerability is studied when the actuator saturation is considered. The sufficient condition for guaranteeing nonfragile robust exponential stabilization of the system is derived by using the method of minimum dwell time. Then, a switching law and the nonfragile state feedback controllers are designed such that the closed‐loop system can be robustly exponentially stabilized at the origin. Next, when some scalar parameters of the closed‐loop system are given, the design issue of the nonfragile state feedback controllers, which aim at enlarging the estimation of domain of attraction for closed‐loop system, is transformed into a convex optimization issue with linear matrix inequalities (LMI) constraints. Finally, an example is given to verify the effectiveness of the proposed method.