Lyapunov-Krasovskii Functional Method Research Articles

Adaptive event-triggered [formula omitted] fuzzy filter design for nonlinear networked systems via asymmetric LKF approach

This paper studies the problem of the fuzzy H∞ filter design for nonlinear networked control systems through event-triggered communication (ETC) scheme. Firstly, an improved adaptive ETC scheme is proposed to save communication resources. Secondly, an asymmetric Lyapunov-Krasovskii functional (LKF) method is introduced in the H∞ performance analysis of filter error systems. Then, a new sufficient condition is obtained to meet the H∞ performance by combining the method with membership-function-dependent approach. Further, a relaxed co-design method of the corresponding filter and event-triggering parameters is obtained. Finally, two numerical examples are provided to verify the advantage of the new approaches.

A resilient optimized dynamic event-triggered mechanism on networked control system with switching behavior under mixed attacks

This paper studies the stability problem and H∞ performance of networked control system (NCS) in the presence of mixed attacks by developing an improved event-triggered mechanism (ETM). Firstly, both aperiodic denial of service (DoS) attacks and random deception attacks are encountered for investigating system dynamic behavior. Then, a resilient optimized dynamic event-triggered mechanism (RODETM) is proposed for reducing the unnecessary costs of system operation and mitigating the impact caused by attacks. On this basis, the standard NCS is reformulated into a switched system under the mixed attacks. Further, using the piecewise Lyapunov-Krasovskii functional method, average dwell time scheme and the linear matrix inequality (LMI) method, some sufficient conditions with control design implementation are obtained, which can ensure the exponential stability with the expected prescribed H∞ performance index of the studied system. Finally, the effectiveness of the proposed approach is demonstrated by using a numerical simulation with comparative analysis.

Distributed Sampled-Data Nonfragile Consensus Filtering Over Sensor Networks With Topology Switching and Transmission Delay

This article concerns the distributed sampled-data nonfragile consensus filter design for a continuous-time linear system with respect to exogenous disturbance. A network of sensor nodes is employed to monitor the plant. The information from each sensor node and its neighbors is aperiodically sampled while collaboratively transmitted in the network, where the phenomena of switching directed topologies and network-induced transmission delay are unavoidably existent. The estimated state of the plant at each node is updated by a consensus of state estimates from its neighbors. By acquiring the sensor output measurement, a Luenberger-type filter is constructed not only to provide robustness against some level of filter gain perturbations, but also to guarantee the asymptotic stability of the resultant filtering error system with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance requirement. Based on algebraic graph theory, nonfragile synthesis technique and Lyapunov–Krasovskii functional method, the filter parameters are characterized in terms of some feasible solutions to certain linear matrix inequalities. The theoretical analysis is validated by numerical simulations.

Positiveness and Finite-Time Control of Dual-Switching Poisson Jump Networked Control Systems With Time-Varying Delays and Packet Drops

This article studies the stochastically finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> control problem for the time-varying delay positive dual-switching Poisson jump networked control systems (TVD-PDSPJ-NCSs) with packet drops. A key issue is that the TVD-PDSPJ-NCSs do not specify the jumping sequence of working processing modes. First, the TVD-PDSPJ-NCSs are modeled for the first time by considering the non-negative total amount of data, work processing modes jumping, and data transmission channel switching of the NCSs. Then, a proper finite-time state feedback controller is designed for the TVD-PDSPJ-NCSs so that the closed-loop dual-switching Poisson jump NCSs are positive, stochastically finite-time bounded, and fulfill the specified <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> disturbance attenuation performance simultaneously. By means of stochastic Lyapunov–Krasovskii functional methods, some sufficient conditions in the form of linear matrix inequalities are derived to obtain the finite-time state feedback controller gain. Furthermore, the optimal solution of the switching law is obtained such that the regulator can select the optimal data transmission channel according to the degree of packet drops. Finally, an application example is given to show the feasibility and validity of the proposed results.

Delay-dependent H∞ dynamic observers for non-linear systems with multiple time-varying delays

The design of dynamic [Formula: see text] observer (DO) for non-linear Lipschitz systems with multiple time-varying delays and disturbances is studied. Sufficient conditions for the existence of these observers are presented in the form of rank equality. Compared to previously published work, the system under consideration includes non-linearity, non-commensurable delay, and external disturbance. Through the use of the Wirtinger inequality and the extended reciprocally convex matrix inequality, new and less conservative delay-dependent conditions in terms of linear matrix inequalities (LMIs) are derived based on the Lyapunov–Krasovskii functional method. Solving these LMIs makes it possible to obtain DO that satisfies an [Formula: see text] performance index. Through two numerical examples in which the comparison with the proportional observer (PO) and the proportional–integral observer (PIO) shows the efficiency of the proposed DO synthesis condition. Furthermore, the results indicate that the DO developed in this paper is more resilient to parameter perturbations.

Hybrid-triggered H∞ Fault Detection for Distributed Time-delay Systems with Communication Quantization Based on T-S Fuzzy Model

In the network environment, the time-triggered mechanism wastes limited bandwidth resources due to the transmission of all sampled data to the network. The event-triggered mechanism may increase system errors due to ignoring factors such as changes in network utilization. In order to reduce the design conservatism, this paper studies the design of a hybrid-triggered H∞ fault detection filter for a class of nonlinear networked control systems described by Takagi-Sugeno (T-S) fuzzy model, and applies quantization techniques in the communication channel. Using the Lyapunov-Krasovskii functional and integral inequality methods, new results on the stability and H∞ performance of fuzzy fault detection systems are presented. In particular, the designed fault detection filter has a specific H∞ noise attenuation level γ. The final simulation results verify the effectiveness of the design.

State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays

In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method.

Distributed cooperative automatic generation control and multi-event triggered mechanisms co-design for networked wind-integrated power systems

The participation of wind energy brings new challenges to the networked power systems. Now, more network nodes compete for limited communication resources. Considering the utilization efficiency of network transmission resources, a novel multi-event triggered mechanisms based distributed cooperative automatic generation control scheme is investigated for networked wind-integrated power systems (NWIPSs). The multi-event triggered mechanisms based distributed wind-integrated power systems modeling method is proposed. By utilizing the Lyapunov-Krasovskii functional method, the sufficient conditions for system asymptotical stability are obtained. Concerning the previous event-triggered method the proposed multi-event triggered method widespread considered the coupling relationship between interconnected subsystems and make full use of each subsystem state information. The numerical example shows that the proposed scheme is feasible and the design of multi-event triggered mechanisms based distributed cooperative automatic generation controller provides less conservatism and stronger robustness.

Fault-tolerant control for T-S fuzzy systems with an aperiodic adaptive event-triggered sampling

This article investigates the exponential stabilization problem for Takagi-Sugeno (T-S) fuzzy systems with actuator faults and aperiodic sampling. First, the fault-tolerant control is designed for T-S fuzzy systems under the given actuator fault model. Second, unlike the existing periodic mechanisms, an improved aperiodic adaptive event-triggered (AET) control scheme is established. The threshold is updated adaptively during the sampling process, which greatly reduces the amount of information transmitted. Then, based on Lyapunov-Krasovskii functional (LKF) method, two sufficient exponential stability conditions are derived. In order to derive the less conservative result, a two-sided looped-functional is constructed. In addition, according to stability conditions and fault-tolerant mechanism, the corresponding sampled-data controller is designed. Finally, a numerical example and a simplified gas turbine system are employed to demonstrate the virtue and effectiveness of application of the proposed scheme.

Asymmetric Lyapunov–Krasovskii functional method for admissibility analysis and stabilisation of T-S fuzzy singular systems with time delay

In this paper, the admissibility analysis and stabilisation of T-S fuzzy singular systems with time delay are studied based on the asymmetric Lyapunov–Krasovskii functional method. The criteria for admissibility analysis and stabilisation are given by using linear matrix inequality, and the conservatism is reduced by combining the membership-function-dependent method. Finally, three examples are given to verify the advantages of the method.

Digital control of a family of time-delay feedforward systems with sparse sampling

For a family of time-delay feedforward systems satisfying a linear growth condition, we study the problem of global asymptotic stabilization by digital state and output feedback, respectively, under arbitrarily sparse sampling. Using the Lyapunov–Krasovskii functional method and the feedback domination design, we construct memoryless sampled-data state and/or output feedback controllers that achieve global asymptotic stability of the hybrid closed-loop systems with large delays. Applications of the sampled-data control schemes are demonstrated through an example with simulations.

Event‐triggered quantized L2−L∞$$ {\mathfrak{L}}_2-{\mathfrak{L}}_{\infty } $$ filtering for neural networks under denial‐of‐service attacks

AbstractThis article deals with the reliable event‐triggered quantized filtering issue for neural networks with exterior interference under denial‐of‐service attacks. In order to lighten the load of communication channels and save network resources, a resilient event‐triggered mechanism and a quantization scheme are employed, simultaneously. By applying a piecewise Lyapunov–Krasovskii functional method, sufficient conditions containing limitations of denial‐of‐service attacks are derived to guarantee that the filter error system is exponentially stable as well as possesses a prescribed disturbance attenuation performance. Then, a co‐design method of the desired quantized filtering gain matrix and event‐triggering parameter can be obtained provided that the linear matrix inequalities have a feasible solution. Finally, the usefulness of the proposed design method is demonstrated by a numerical example.

Robust Finite-Time Control of Discrete-Time Switched Positive Time-Varying Delay Systems with Exogenous Disturbance and Their Application

Many practical systems can be modeled in terms of uncertainties, which refer to the differences or errors between actual data and mathematical simulations. However, systems including slight uncertainties and exogenous disturbances may lead to the instability of those systems. Besides, the behavior of systems is preferable to investigate within a prescribed bound over a fixed time interval. Therefore, in this paper, we study a robust finite-time control of discrete-time linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance. A distinctive feature of this research is that the considered systems consist of finite-time bounded subsystems and finite-time unbounded subsystems. A class of quasi-alternative switching signals is validly designed to analyze the mechanism and switching behaviors of the systems among their subsystems. By utilizing a copositive Lyapunov–Krasovskii functional method combined with the slow mode-dependent average dwell time and the fast mode-dependent average dwell time switching techniques, new sufficient conditions containing several symmetric negative-definite matrices are derived to guarantee robust finite-time control of the systems. These results are applied to a water-quality controllability model in streams to the standard level. Finally, the consistent results between the theoretical analysis and the corresponding numerical simulations are shown.

Sliding Mode Observer-Based Fault Detection in Continuous Time Linear Switched Systems

This paper studies the problem of fault detection for continuous time linear switched systems in the presence of disturbance. For this purpose, a fault detection sliding mode observer approach is designed to generate the residual signal. To minimize the effect of disturbance from the residual, the problem is formulated into H∞ filtering technique to increase more robustness. To deal with the issue of the switched systems stability, the Lyapunov-Krasovskii functional method is utilized along with average dwell time, and linear matrix inequalities are formulated to derive the sufficient conditions. The residual signal is evaluated, and an adaptive threshold is computed for both modes of the switched system. Finally, a simulation example for a case study of boost converter and a numerical example with both abrupt and incipient faults are illustrated to prove the efficacy of the proposed method.

Stability analysis of hybrid time-delay systems using homogeneity property

In this paper, stability analysis is studied for hybrid time-delay systems (HTDSs) with homogeneity. Using Lyapunov–Krasovskii functional method, a novel and relaxed condition is derived to analyze pre-asymptotic stability of the considered systems with homogeneity. Then, the connections of solutions are established between the systems with different sizes. Based on the established connections, some homogeneous properties are introduced to analyze stability of the HTDSs with different sizes or degrees, and then some necessary and sufficient stability conditions are obtained. Finally, numerical examples are provided to show the effectiveness of the results obtained in this paper.

Position Tracking Control of Robotic System with Time-varying Delay and Dead-zone

This paper studies the position tracking control problem of nonlinear robotic system subject to time-varying state delay and input dead-zone. The input dead-zone and unknown external disturbance are regarded as the lumped disturbance and a sliding mode disturbance observer is designed. In order to ensure the stability of the robotic system with time-varying state delay, a position tracking controller based on auxiliary position tracking error functions is designed. Considering the estimated error of the sliding mode disturbance observer, a gain adaptive law is designed to further improve the position tracking accuracy of the system. The stability of the proposed controller is theoretically proved by Lyapunov-Krasovskii function method, and the effectiveness of the controller is verified by comparative simulations. The proposed control method can achieve stable and accurate position tracking of the robotic system with simultaneous time-varying state delay and input dead-zone.

Sampled-Data Delayed Output Feedback Control of a Class of Nonlinear Systems

This letter presents a sampled-data control strategy for robust stabilization of a family of uncertain nonlinear systems via delayed output signals. Instead of building dynamic observers,we use an output signal sampled at the current time and delayed outputmeasurements at the previous n -1 sampling points to design sampleddata controllers, which are easier for implementation by computer. Under a linear growth condition, it is proved that global robust stabilization is achievable by sampleddata delayed output feedback. The robust stability analysis of the hybrid closed-loop system with delays is conducted by the Lyapunov-Krasovskii functional method.

Dynamic output feedback control for networked control systems: A sum-based discrete event-triggered approach

This paper investigates the event-based dynamic output feedback control for networked control system with actuator failures. A novel sum-based discrete event-triggered mechanism (SDETM) is proposed, whose triggering condition includes not only the current sample of system states but also previous samples. With the proposed SDETM, a dynamic output feedback controller (DOFC) is developed under a general networked control system (NCS) structure. We consider a general system structure where two network channels are involved, and the proposed SDETM is employed to both networks to extensively save network resources. A novel stability criteria is established for the closed-loop system based on the Lyapunov-Krasovskii functional method. By using the Cone-complimentarity Linearization (CCL) approach, sufficient conditions are derived to co-design the DOFC and triggering parameters. The effectiveness and advantage of the proposed method is verified by a satellite control system.

Event-Triggered Zero-Gradient-Sum Distributed Algorithm for Convex Optimization with Time-Varying Communication Delays and Switching Directed Topologies

Nowadays, distributed optimization algorithms are widely used in various complex networks. In order to expand the theory of distributed optimization algorithms in the direction of directed graph, the distributed convex optimization problem with time-varying delays and switching topologies in the case of directed graph topology is studied. The event-triggered communication mechanism is adopted, that is, the communication between agents is determined by the trigger conditions, and the information exchange is carried out only when the conditions are met. Compared with continuous communication, this greatly saves network resources and reduces communication cost. Using Lyapunov-Krasovskii function method and inequality analysis, a new sufficient condition is proposed to ensure that the agent state finally reaches the optimal state. The upper bound of the maximum allowable delay is given. In addition, Zeno behavior will be proved not to exist during the operation of the algorithm. Finally, a simulation example is given to illustrate the correctness of the results in this paper.

Global Input Delay Tolerance of MIMO Nonlinear Systems under Nonsmooth Feedback: A Homogeneous Perspective

In this paper, we tackle the problem of when a globally asymptotically stabilizable (GAS) nonlinear system by either state or output feedback is globally tolerable with respect to input delay. We focus on the case when the continuous system is not stabilizable by linear or smooth feedback, and thus local exponential stabilizability (LES) is not fulfilled. With the aid of the Lyapunov-Krasovskii functional method and weighted homogeneity, we prove that for a multi-input-multi-output (MIMO) nonlinear system with homogeneous degree zero, global asymptotic stabilizability by nonsmooth but H&#x00F6;lder continuous state or output feedback implies global asymptotic stability (GAS) of the closed-loop system with input delay, i.e., the property of global input delay tolerance (GIDT). We then illustrate applications of the obtained GIDT results to significant classes of time-delay nonlinear systems with uncontrollable/unobservable linearization, including but not limited to a chain of nonlinear integrators, higher-order systems with a lower-triangular or upper-triangular structure, and beyond.