Lyapunov-Krasovskii Functional Method Research Articles

An improved exponential stability analysis method for discrete‐time systems with a time‐varying delay

AbstractExponential stability analysis of discrete‐time nonlinear systems with a time‐varying delay is concerned in this article. The main contribution of this article lies in proposing an improved stability analysis method called a delay‐mode‐based functional method. The improved method is presented by weakening a condition in the Lyapunov–Krasovskii functional method. With the help of the new method, less conservative exponential stability criteria of discrete‐time linear systems with a time‐varying delay are obtained and two classical examples are given to show that the delay‐mode‐based functional method is effective.

Sampled-data control of a class of time-delay nonlinear systems via memoryless feedback

We prove that under a linear growth condition, a family of time-delay nonlinear systems is globally stabilizable by memoryless sampled-data state and output feedback, respectively, if the input delay and sampling period are not too big although the state delays are permitted to be large. The proofs rely on the construction of sampled-data feedback controllers and the Lyapunov–Krasovskii functional method. The designed memoryless controllers achieve global asymptotic stabilization of the hybrid closed-loop systems with time-delay and are easily implementable by computers owing to their discrete-time and delay-free nature.

Adaptive Event-Triggered Synchronization of Uncertain Fractional Order Neural Networks with Double Deception Attacks and Time-Varying Delay.

This paper investigates the problem of adaptive event-triggered synchronization for uncertain FNNs subject to double deception attacks and time-varying delay. During network transmission, a practical deception attack phenomenon in FNNs should be considered; that is, we investigated the situation in which the attack occurs via both communication channels, from S-C and from C-A simultaneously, rather than considering only one, as in many papers; and the double attacks are described by high-level Markov processes rather than simple random variables. To further reduce network load, an advanced AETS with an adaptive threshold coefficient was first used in FNNs to deal with deception attacks. Moreover, given the engineering background, uncertain parameters and time-varying delay were also considered, and a feedback control scheme was adopted. Based on the above, a unique closed-loop synchronization error system was constructed. Sufficient conditions that guarantee the stability of the closed-loop system are ensured by the Lyapunov-Krasovskii functional method. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

Stability of stochastic delay switched neural networks with all unstable subsystems: A multiple discretized Lyapunov-Krasovskii functionals method

This paper considers switching stochastic delay neural networks (SSDNNs) with all unstable subsystems. By using discretized Lyapunov-Krasovskii functions (DLKFs) combined with the dwell time method, exponential stability of SSDNNs with all unstable subsystems are analyzed, and several novel stability criteria in mean square are obtained. Comparing with the existing works, our results focus on all unstable subsystems rather than other combinations such as all stable or partially stable subsystems, which is of more research significance. Finally, the correctness of the conclusion is checked by the feasible solutions of two numerical examples.

A Novel Asymmetric Lyapunov–Krasovskii Functional Method to Stability for T–S Fuzzy Systems with Time-Varying Delay

A Novel Asymmetric Lyapunov–Krasovskii Functional Method to Stability for T–S Fuzzy Systems with Time-Varying Delay

Finite-time filtering of T-S fuzzy semi-Markov jump systems with asynchronous mode-dependent delays

This paper studies the finite-time filter design of semi-Markov jump system by Takagi-Sugeno (T-S) fuzzy rules. Asynchronous mode-dependent delays are concerned to describe more practical random features, which implies that the semi-Markov process of system state is different from another semi-Markov process of mode-dependent time-varying delays. With the help of model transformation as well as mode-dependent Lyapunov-Krasovskii function method, sufficient criteria are first established for maintaining finite-time passivity performance of filtering errors. Then, the matrix technique is employed to synthesize the filter gain design. In the end, the applicableness and effectiveness of our developed results are confirmed by an illustrative example.

Finite-time Stochastic Stability and Stabilization for Uncertain Discrete-time Stochastic Systems with Time-varying Delay

This paper deals with the problems of finite-time stochastic stability and stabilization for discrete-time stochastic systems with parametric uncertainties and time-varying delay. Using the Lyapunov-Krasovskii functional method, some sufficient conditions of finite-time stochastic stability for a class of discrete-time stochastic uncertain systems are established in term of matrix inequalities. Then, a new criterion is proposed to ensure the closed-loop system is finite-time stochastically stable. The controller gain is designed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

Stability of nonlinear distributed delay system with parameter uncertainties: Integral‐based event‐triggered impulsive control strategy

AbstractThis article investigates the stability of nonlinear uncertain distributed delay system via integral‐based event‐triggered impulsive control (IETIC) strategy. First, a IETIC mechanism is presented to reduce the redundant data transmission over the system, in which the integral‐based event‐triggered mechanism uses the integration of system states over a time period in the past. Second, a new lemma is proposed to eliminate the Zeno behavior of the established model through the IETIC mechanism. Third, a novel Lyapunov–Krasovskii functional (LKF) method related to probability density function is constructed to guarantee the stability of the established model based on LMI conditions, where a probability density function is introduced as a distributed delay kernel. Compared with existing methods, the constructed novel LKF method is less conservative or requiring less number of decision variables. Numerical examples are further provided to confirm the effectiveness and advantages of the proposed approach.

On qualitative behaviors of nonlinear singular systems with multiple constant delays

This paper deals with some qualitative properties of a class of nonlinear singular systems with multiple constant delays. Via the Lyapunov-Krasovskii functional (LKF) method and integral inequalities, we obtain some new sufficient conditions which guarantee that the considered systems are regular, impulse-free and exponentially stable. Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB software. By this work, we extend and improve some results of the past literature.

Event‐based impulsive consensus for delayed multi‐agent systems

AbstractThis paper focuses on the average consensus problem for delayed nonlinear multi‐agent systems. To reduce unnecessary energy consumption, a novel event‐triggered impulsive control mechanism is adopted, in which the impulsive time series is determined by some pre‐designed events. Simultaneously, the Zeno‐behavior of the event‐triggering time series is excluded. By using Lyapunov–Krasovskii functional method as well as impulsive control theory, an easy‐to‐check sufficient criterion is derived to ensure the average consensus of the considered nonlinear multi‐agent systems. Finally, the applications and effectiveness of the obtained results is validated with a simulation example.

Aperiodically intermittent pinning outer synchronization control for delayed complex dynamical networks with reaction-diffusion terms

In this paper, we mainly study the outer synchronization problem of complex dynamical networks (CDNs) involving delays and reaction-diffusion terms by aperiodically intermittent pinning control (AIPC). By using piecewise function and Lyapunov-Krasovskii functional method, some criteria for the complete and exponential outer synchronization of the corresponding CDNs with and without the coupling delay are obtained. Furthermore, two numerical examples are provided to illustrate the effectiveness of the obtained results.

Quantized control for extended dissipative synchronization of chaotic neural networks: A discretized LKF method

This work focuses on the extended dissipative synchronization problem for chaotic neural networks with time delay under quantized control. The discretized Lyapunov–Krasovskii functional method, in combination with the free-weighting matrix approach, is employed to obtain an analysis result of the extended dissipativity with low conservatism. Then, with the help of several decoupling methods, a computationally tractable design approach is proposed for the needed quantized controller. Finally, two examples are provided to illustrate the usefulness of the present analysis and design methods, respectively.

A novel control Lyapunov-Krasovskii functional methodology for simultaneous stabilization of a set of multiple time-delays nonlinear systems

This paper considers the simultaneous stabilization of a set of nonlinear systems, that involve uncertain nonlinearities besides multiple time-varying delays in the states. Under the assumption that the upper bounds of delays are known, a memoryless simultaneously stabilizing state feedback controller is presented by proposing a control Lyapunov-Krasovskii functional (CL-KF) method. As required to establish the CL-KF approach, a systematic procedure is given to construct CL-KFs for the systems under consideration. By the obtained CL-KFs, a common stabilizing state feedback control law is established to drive all the systems to the origin. Examples are finally given to verify the benefit of the proposed design method.

Observer-based defense control for networked Takagi-Sugeno fuzzy systems against asynchronous DoS attacks

This article investigates the defense control problem for sampled-data Takagi-Sugeno (T-S) fuzzy systems with multiple transmission channels against asynchronous denial-of-service (DoS) attacks. Firstly, a new switching security control method is proposed to tolerate the asynchronous DoS attacks that act independently on each channel. Then, based on switching strategy, the resulting augmented sampled-data system can be converted into new switched systems including several stable subsystems and one open-loop subsystem. Besides, by applying the piecewise Lyapunov-Krasovskii (L-K) function method, membership functions (MFs) dependent sufficient conditions are derived to ensure the exponential stability of newly constructed switching systems. Moreover, quantitative relations among the sampling period, the exponential decay rate, and the rate of all channels being fully attacked and not being completely attacked are established. Finally, simulation examples show the effectiveness of the developed defense control approach.

An Asymmetric Lyapunov–Krasovskii Functional Method on Stability and Stabilization for T-S Fuzzy Systems With Time Delay

This article presents a new asymmetric Lyapunov–Krasovskii functional method on the stability and stabilization of Takagi–Sugeno fuzzy systems with time delay. For the reduction of conservativeness, combining the method with the membership-function-dependent approach, we propose a novel delay-dependent stability condition in the form of linear matrix inequalities. Based on the condition, we further obtain a novel condition of stabilization. At the end, we provide two numerical examples to verify the advantage of the stability and stabilization approaches, respectively.

Non-fragile distributed mode-dependent dissipative state estimation of uncertain Markov jump systems over sensor networks

This paper considers the non-fragile distributed state estimation problem for Markov jump systems over sensor networks based on dissipative theory. Moreover, both state estimator gain variations and parameter uncertainties are assumed to be with mode-dependent for more practical modeling. On the basis of stochastic analysis and Lyapunov–Krasovskii function method, sufficient conditions with desired mode-dependent estimators are established such that the prescribed dissipative performance can be achieved. In the end, the effectiveness and applicability of the developed scheme is confirmed via the illustrative example.

Finite-time Stabilization of Switched Positive Systems with Time-varying Delays and Actuator Saturation

In this paper, the finite-time stabilization for a class of switched positive systems with time-varying delays and actuator saturation under average dwell time switching is investigated. Through multiple copositive Lyapunov-Krasovskii functionals method, the sufficient conditions for finite-time bounded of continuous-time case are given, and the appropriate switching rules and state feedback controllers are presented together. Moreover, the convex hull technique is employed to deal with actuator saturation. Finally, an illustrative example is given to show the effectiveness of the proposed method.

Finite-Time Almost Sure Stability of a Markov Jump Fuzzy System With Delayed Inputs

This article addresses the problem of finite-time almost sure stability, where the system is with Markov jump parameters and delayed inputs. With using Gronwall’s inequality and strong law of large numbers for Markov chains, finite-time bounded criteria and finite-time stability criteria are derived by Lyapunov–Krasovskii functional method. Moreover, a finite-time stability criterion in form of linear matrix inequality is given to design the controller gain. The obtained results are applied to finite-time sampled-data control of a truck-trailer system and finite-time control of a Markov jump mass-spring model with delayed inputs.

Exponential synchronization of memristive neural networks with inertial and nonlinear coupling terms: Pinning impulsive control approaches

This paper investigates exponential synchronization for memristive neural networks (MNNs) with inertial and nonlinear coupling terms. Two novel hybrid mode-dependent pinning impulse control approaches are proposed, one is adaptive element-selection and pinning a part of elements in each identical node, and the other is fixed node-selection and pinning a part of identical nodes. By introducing appropriate variable substitution, the initial second-order state derivative model for MNNs is transformed into two first-order derivative equations. Then, through introducing average impulsive interval, Lyapunov–Krasovskii functional method, inequality techniques, and extended comparison principle, some corresponding exponential synchronization conditions are presented, which enrich and extend some published results. Finally, simulations are given to illustrate the exponential synchronization conditions.

Practical stability of time‐varying positive systems with time delay

This paper considers the problem of practical stability for time-varying positive systems with time delay. For both non-linear time-varying positive systems and linear time-varying positive (LTVP) systems with time delay, sufficient conditions on practical stability are derived by the max-separable Lyapunov-Krasovskii (L–K) functional method. Then based on the obtained results, an effective method for designing a desired controller in terms of state feedback and state feedback with input delay is established for LTVP systems with time delay. At the end, numerical examples are presented to illustrate the effectiveness of our results.