Suitable Lyapunov-Krasovskii Functionals Research Articles

Adaptive control for a class of stochastic nonlinear time-delay systems with unknown control coefficients

This paper mainly investigates the adaptive state feedback control problem for a class of stochastic nonlinear systems with time-delay and unknown control coefficients. The proposed control scheme leverages the dynamic gain technology and Nussbaum function to develop a state feedback controller, aiming to simplify its implementation and eliminate the influence of unidentified time-varying control coefficients. Through the utilization of suitable Lyapunov–Krasovskii (L–K) functionals and stochastic stability theories, it is demonstrated that the designed control mechanism guarantees the boundedness in probability for all closed-loop signals, ultimately regulating the state of the plant to zero. The availability and superiority of the developed adaptive management strategy are further certified through simulation results.

On exponential and L2-exponential stability of continuous-time delay-difference systems

In this paper, the exponential stability (ES) and L2-exponential stability (L2-ES) of continuous-time delay-difference systems are studied. Firstly, the relationship between ES and L2-ES of the studied system is systematically presented. Secondly, a novel Lyapunov stability theorem is proposed to test both the ES and L2-ES with a guaranteed convergence rate of the system. Then, for a particular class of delay-difference systems with both point delays and distributed delays having exponential integral kernels, some stability criteria based on linear matrix inequalities (LMIs) are established by selecting suitable Lyapunov-Krasovskii functionals (LKFs) and using a delay decomposition technique. Finally, a numerical example is worked out to illustrate the effectiveness of the theoretical results.

Adaptive neural dynamic surface control for nonstrict feedback systems with state delays

AbstractThis article focuses on a class of nonstrict feedback systems with input delay, state delays and time‐varying full‐state constraints by proposing an adaptive neural control scheme. To overcome the problems of all state variables effected by time‐varying constraints, the asymmetric time‐varying barrier Lyapunov functions are constructed. The influence of state delays and input delay is eliminated by employing suitable Lyapunov–Krasovskii functionals. Additionally, the process of controller design is based on backstepping method and the unknown functions can be approximated by radial basis function neural networks. Moreover, the problem of repeated differentiations for nonlinear components during controller design is hugely simplified by taking advantage of the dynamic surface control method. The boundness of all the closed‐loop signals can be ensured by the designed controller. Finally, two numerical simulations illustrate that the proposed adaptive neural control scheme is effective.

Observer-based finite-time H∞ control for discrete-time singular Markovian jump systems with asynchronous modes

The asynchronous observer-based finite-time [Formula: see text] control problem for discrete-time singular Markovian jump systems with time-varying delays is studied, where the asynchronism of the controller and observer with respect to the original system is fully taken into consideration. By the use of finite-time analysis theory and the construction of suitable Lyapunov-Krasovskii functionals, sufficient conditions to determine the closed-loop error system is singular stochastic finite-time boundedness are given with [Formula: see text] performance level. Then, by applying linear matrix inequalities, the desired observer parameters and controller parameters can be computed. Finally, the effectiveness of our proposed method is confirmed by simulation.

General single/multiple integral inequalities and their applications to stability of time-delay systems

This paper is concerned with the stability of time delay systems. A new type of multiple integral inner product and a new class of multiple integral inner product space are firstly introduced. Based on them, general single/multiple integral inequalities are developed, and some previous integral inequalities including single and multiple integral inequalities can be regarded as their special cases. Secondly, suitable Lyapunov–Krasovskii functionals (LKF) are constructed. On the basis of the proposed integral inequalities, the derivative of the LKF can be gauged more accurate than those in the literature. As a result, some improved stability criteria of time-delay systems are formulated in terms of linear matrix inequalities. Through two numerical examples, it is shown that these criteria can provide larger delay upper bounds than some existing ones, showing the effectiveness and superiority of the proposed method.

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>

Synchronization of complex dynamical networks subjected to actuator faults and periodic scaling attacks using probabilistic time-varying delays

In this paper, the synchronization problem of complex dynamical networks (CDNs) subjected to actuator faults and periodic scaling attacks using probabilistic time-varying delays is investigated. In order to handle the fault effects in actuators of proposed complex networks, an actuator fault model is considered. The major objective of this paper is to construct a memory state feedback controller with time-varying actuator faults that are asymptotically synchronized in the mean square sense to defend against periodic scaling attacks. By establishing suitable Lyapunov-Krasovskii functionals and applying Wirtinger-based integral inequality, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for the proposed system. Moreover, a time-varying delay is supposed to depend on probabilistic distribution conditions. Thus, the resulting criteria that emerge are based on the amount of the delay as well as the probability that the delay will have values at certain intervals. At last, the efficiency of our proposed work is demonstrated by two numerical simulations.

Event-triggered gain-scheduling dissipative synchronization control for switched neural networks under state-dependent switching

The dissipative synchronization problem of delayed Markov jump switched neural networks (MJSNNs) under state-dependent switching by the event-triggered gain-scheduling control scheme is studied in this paper. By the introduction of a Markov jump model, which is used to depict the random variation wherein the connection of MJSNNs, the issues we study can take more generality. Via constructing suitable Lyapunov–Krasovskii functionals (LKFs) and applying some matrix inequality scaling methods, sufficient conditions for dissipative synchronization of delayed MJSNN are established. According to such criteria, the event-triggered gain-scheduling control scheme is adopted to design a controller with less terminal communication costs. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Admissibility Analysis and Control for Discrete-Time Singular Systems with Interval Time-Varying Delay

This paper mainly investigates an admissibility analysis and controller design problem for an uncertain discrete-time singular system with delayed states. The time-varying delay is within an interval whose lower bound may be greater than zero. Using a modified finite sum inequality and choosing a suitable Lyapunov-Krasovskii function, we derive a set of LMI-based sufficient delay-dependent conditions for the admissibility analysis and controller synthesis problem, respectively. In the end, a numerical example shows the effectiveness and validity of the proposed approach.

Direct quaternion method-based stability criteria for quaternion-valued Takagi-Sugeno fuzzy BAM delayed neural networks using quaternion-valued Wirtinger-based integral inequality

<abstract><p>This paper investigates the global asymptotic stability problem for a class of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. By applying Takagi-Sugeno fuzzy models, we first consider a general form of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. Then, we apply the Cauchy-Schwarz algorithm and homeomorphism principle to obtain sufficient conditions for the existence and uniqueness of the equilibrium point. By utilizing suitable Lyapunov-Krasovskii functionals and newly developed quaternion-valued Wirtinger-based integral inequality, some sufficient criteria are obtained to guarantee the global asymptotic stability of the considered networks. Further, the results of this paper are presented in the form of quaternion-valued linear matrix inequalities, which can be solved using the MATLAB YALMIP toolbox. Two numerical examples are presented with their simulations to demonstrate the validity of the theoretical analysis.</p></abstract>

Global Asymptotic Stability of Competitive Neural Networks with Reaction-Diffusion Terms and Mixed Delays

In this article, a new competitive neural network (CNN) with reaction-diffusion terms and mixed delays is proposed. Because this network system contains reaction-diffusion terms, it belongs to a partial differential system, which is different from the existing classic CNNs. First, taking into account the spatial diffusion effect, we introduce spatial diffusion for CNNs. Furthermore, since the time delay has an essential influence on the properties of the system, we introduce mixed delays including time-varying discrete delays and distributed delays for CNNs. By constructing suitable Lyapunov–Krasovskii functionals and virtue of the theories of delayed partial differential equations, we study the global asymptotic stability for the considered system. The effectiveness and correctness of the proposed CNN model with reaction-diffusion terms and mixed delays are verified by an example. Finally, some discussion and conclusions for recent developments of CNNs are given.

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

This paper concentrates on the robust stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay. Firstly, by using a suitable Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems is proposed. Then, based on the above stability conditions, the robust delay-dependent and order-dependent stability conditions for the uncertain systems are discussed. Moreover, in order to stabilize the nominal and uncertain systems, state feedback controllers are also derived with the help of the presented stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.

Finite-time asynchronous [formula omitted] fault-tolerant control for nonlinear hidden markov jump systems with actuator and sensor faults

This paper studies the H∞ fault-tolerant control problem for a class of conic-type nonlinear Markov jump systems with sensor and actuator faults as well as unknown disturbances. Firstly, the hidden Markov model is introduced to deal with the asynchronous problem existing in the control systems. By selecting suitable Lyapunov-Krasovskii function, linear matrix inequalities techniques are applied to obtain the H∞ fault-tolerant controller. A new condition of the state feedback H∞ fault-tolerant controller with actuator faults and sensor faults is presented. The proposed control strategy can not only ensure the finite-time boundness of the closed loop system, but also guarantee the required H∞ performance. Lastly, the availability of the design scheme is validated by a simulation example.

An augmented approach to absolute stability for uncertain Lur'e system with time‐varying delay

This paper investigates the absolute stability criteria of Lur'e system with time‐varying delays, uncertainties, and sector bounded nonlinearities. By constructing suitable Lyapunov–Krasovskii functionals (LKFs) and utilizing some useful mathematical techniques, an improved delay‐dependent stability criterion is introduced in Theorem 1. Based on the result of Theorem 1, a further enhanced criterion is proposed in Theorem 2 by employing the augmented zero equality approach. Finally, two numerical examples show the improved performance of the criteria by comparing maximum delay bounds.

Exponential state estimation for reaction-diffusion inertial neural networks via incomplete measurement scheme

ABSTRACT In this paper, the problem of exponential state estimation for inertial neural networks with reaction-diffusion term (RDINNs) via incomplete measurement scheme is investigated. Unlike the full measurement method, this method estimates the system by measuring the state of partially available neurons. First, by constructing an appropriate variable substitution, the second-order system is transformed into a first-order one. Then, a suitable Lyapunov-krasovskii function (LKF) is constructed, and sufficient conditions for the stability of the system are obtained . Finally, the practicality and effectiveness of the proposed method is further verified by two numerical examples.

Distributed event‐triggered cooperative H∞ load frequency control for interconnected networked power systems

Interconnected communication time-varying delays between subsystems for large scale distributed networked power systems (DNPSs) are studied in this work. Distributed event-triggered mechanisms-based interconnected DNPSs and their cooperative H ∞ stability control strategy are proposed for load frequency control in multi-area interconnected power systems. Considering the distributed interconnected DNPSs, the subsystems have their own state time-delay, and there are time-varying delays and package dropout in subsystems interconnection; in order to reduce the amount of transmitted signals and improve the efficiency of the network communication resource, a distributed event-triggered mechanisms-based system model and a novel design method for networked cooperative H ∞ control strategy are proposed. Based on the Lyapunov stability analysis method, a suitable Lyapunov Krasovskii function is constructed, and the distributed controller design scheme is derived based on the feasible solution of linear matrix inequality (LMI). The sufficient conditions for the system asymptotical stability is given. Finally, a four-area networked interconnected hybrid power system is considered and the system performance under networked load fluctuations is analysed; the simulation results show that the proposed scheme is feasible and effective.

Synchronization of nonidentical complex dynamical networks with unknown disturbances via observer-based sliding mode control

This paper studies globally asymptotical synchronization of nonidentical complex dynamical networks in presence of time delays and unknown disturbances. Based on the idea of sliding mode control, we propose the observer-based sliding mode control scheme to deal with the synchronization of nonidentical complex dynamical networks, where the unknown disturbances are estimated by the disturbance observer. Moreover, the designed sliding mode controller not only guarantee the reachability of the integral sliding surface but also overcome the influence of the disturbances in the control channel. Then, some sufficient conditions of globally asymptotical synchronization are derived via constructing some suitable Lyapunov–Krasovskii functionals and using linear matrix inequality technique. Finally, an example is given to demonstrate the applicability and the effectiveness of our method.

Finite-time asynchronous dissipative filtering of conic-type nonlinear Markov jump systems

In the present study, the finite-time asynchronous dissipative filter design problem for the Markov jump systems with conic-type nonlinearity is studied. The hidden Markov model can describe the asynchronism embodied in the system modes and the filter modes reasonably. Moreover, a suitable Lyapunov-Krasovskii function is utilized and linear matrix inequalities are applied to obtain adequate conditions. These techniques guarantee the finite-time boundedness and strict dissipativity of the filtering error dynamic system. Furthermore, the design problems of the passive filter and the H∞ filter are studied by adjusting the three parameters $${\cal U}$$ , $${\cal G}$$ and $${\cal V}$$ . Finally, the filter gains and the optimal index α* are obtained and the correctness and feasibility of the designed approach are verified by a simulation example.

Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays

Abstract This paper is concerned with a class of bidirectional associative memory (BAM) neural networks with discontinuous activations and time-varying delays. Under the basic framework of differential inclusions theory, the existence result of solutions in sense of Filippov solution is firstly established by using the fundamental solution matrix of coefficients and inequality analysis technique. Also, the boundness of the solutions can be estimated. Secondly, based on the non-smooth Lyapunov-like approach and by construsting suitable Lyapunov–Krasovskii functionals, some new sufficient criteria are given to ascertain the globally exponential stability of the anti-periodic solutions for the proposed neural network system. Furthermore, we have collated our effort with some previous existing ones in the literatures and showed that it can take more advantages. Finally, two examples with numerical simulations are exploited to illustrate the correctness.

Event-triggered finite-time adaptive neural control for nonlinear non-strict-feedback time-delay systems with disturbances

This paper focuses on the tracking problem for a class of nonlinear time-delay systems with external disturbances in a non-strict-feedback structure, and an event-trigger-based finite-time adaptive neural controller is designed. Suitable Lyapunov-Krasovskii functionals are constructed to deal with the time-delay terms in this system. Combining the structural property of radial basis function neural networks and backstepping methodology, the design difficulty from the non-strict-feedback structure of the system is solved. A finite-time prescribed performance function is introduced to drive the tracking error to a small neighborhood of the origin in a finite time. The proposed event-triggered control scheme has a larger threshold than that of the fixed-threshold scheme to reduce the communication burden and ensure that all of the signals of the closed-loop system are semi-globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the proposed scheme.