Nonfragile power and frequency control in islanded microgrids under abnormal asynchronous stochastic cyber attacks

In this paper, we focus on the real power sharing and frequency regulation of distributed generators in islanded microgrids with abnormal asynchronous stochastic cyber attacks, which is of great significance to the information security and stable operation of microgrids. Firstly, considering the possible cyber attacks in the communication network, a distributed non-fragile controller with coupled memory delay is proposed according to the nonperiodic sampled-data control. Then, the construction of delay-dependent two-sided looped-functional makes the Lyapunov-Krasovskii functional contain more delay and sampling information and relaxes constraints on free matrices. In addition, based on the enhanced integral inequality technique and the linear convex combination method, a sampling-based consensus protocol is presented to solve the issues of real power sharing and frequency regulation in the islanded microgrids. Finally, to verify the effectiveness and feasibility of the designed control strategy, a modified IEEE 34-bus test system is used for the experiment.

Data-driven control for multi-rate multi-input/single-output systems

For the next generation of manufacturing, represented by Industrie 4.0, a multi-input controller is designed directly from controlled data, without using the mathematical plant model, where the ratio between the D/A conversion of multiple inputs and the A/D conversion of a single output is non-uniquely. With the proposed method, the fixed-structured controller is optimally designed by solving a model reference problem using one-shot data. Furthermore, to eliminate inter-sample ripples emerged by input oscillation, the deviation of the control inputs is also evaluated using the proposed method. As a result, a non-ripple data-driven controller is achieved. Numerical examples show that the proposed multi-rate data-driven method is superior than the conventional single-rate method.

Non-fragile sampled-date dissipative analysis for uncertain T–S fuzzy time delay system with actuator saturation

In this paper, non-fragile fuzzy sampled-data control is used to analyze the dissipation of uncertain time-varying delay T–S fuzzy system under actuator saturation. First, this paper builds a novel augmented Lyapunov–Krasovskii functional that is more flexible. It involves complete information about the relevant sampled-data patterns. Second, the use of Wirtinger-based integral inequality and Newton–Leibniz formulas yields less conservative results. Next, we discuss the sufficient conditions of the dissipative performance for T–S model, then use the linear matrix inequality (LMI) to give the non-fragile fuzzy sampled-data controller with actuator saturation. Finally, the routine examples show that the advanced approach is effective and feasible and has certain advantages.

Non-fragile synchronization of complex dynamical networks with hybrid delays and stochastic disturbance via sampled-data control

This paper focuses on the global synchronization issue for a class of the complex dynamical networks (CDNs) with hybrid delays and stochastic disturbance. The hybrid delays consider two forms: discrete-time coupling delays and distributed coupling delays. The non-fragile sampled-data control protocol, which is allowed to norm-bounded uncertainty, is considered for the first time in this paper. Next, by applying a new augmented Lyapunov-Krasovskii functional (LKF), with the aid of the convex combination method and the stochastic analysis technique, a less conservative condition is derived to ensure that the considered CDNs can achieve the global synchronization with hybrid delays and stochastic disturbance under a non-fragile sampled-data control strategy. Finally, there exists three simulation examples to verify the effectiveness and advantages of the analytical results.

Finite-time non-fragile H∞ sampled-data control for uncertain T-S fuzzy system with time-varying delay and nonlinear perturbation subject to Markovian jump

This paper focuses on studying the finite-time non-fragile H_∞ sampled-data control of uncertain T-S fuzzy time-varying delay system with nonlinear perturbation and Markovian jump parameters. We first construct a different Lyapunov-Krasovskii functional that plays a key role to fully capture the available characteristics of sampling period. Second, based on the Lyapunov-Krasovskii functional approach, free weighting matrix method and a novel efficient inequality technique, less conservative sufficient conditions are established, which make stochastic fuzzy system achieve finite-time boundedness and finite-time H_∞ boundedness with an optimized performance. Then, the desired multiplicative non-fragile sampled-data control gains can be obtained by solving the linear matrix inequalities. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method.

Sampled-data control for linear time-delay distributed parameter systems

Some real systems have spatiotemporal dynamics and are time-delay distributed parameter systems (DPSs). The existence of time-delay may lead to system instability. The analysis and design of DPSs with time-delay is essentially more complicated. To take into account the factor of time-delay and fully enjoy the benefits of the digital technology in control engineering, it is a theoretical and practical value to consider the sampled-data control (SDC) problem of DPSs with time-delay. However, there are few attempts to solve the SDC problem of time-delay DPSs. In this paper, we introduce a SDC for linear time-delay DPSs described by parabolic partial differential equations (PDEs). A SDC design is developed in the formulation of spatial linear matrix inequalities (LMIs) by constructing an appropriate Lyapunov functional, which can stabilize exponentially the time-delay DPSs. This stabilization condition can be applied to either slowing-varying time delay or fast-varying one. Finally, simulation results of a numerical example are provided to illustrate the effectiveness of the proposed method.

Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications

This paper investigates the finite time stability (FTS) for nonlinear impulsive sampled-data systems. By constructing an appropriated Lyapunov function and employing average impulsive interval (AII) method, some FTS criteria for the nonlinear impulsive sampled-data systems are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. The hybrid controller including sampled-data controller and impulsive controller is designed via the established LMIs. Moreover, the impulse effect considered in this paper including stabilizing impulse and destabilizing impulse. Our developed results are less conservative than the recent work in the literature. Finally, two numerical examples are provided to show the applications of the proposed criteria.

Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach

This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.

Guaranteed cost consensus protocol design for linear multi-agent systems with sampled-data information: An input delay approach

To investigate the energy consumption involved in a sampled-data consensus process, the problem of guaranteed cost consensus for sampled-data linear multi-agent systems is considered. By using an input delay approach, an equivalent system is constructed to convert the guaranteed cost consensus problem to a guaranteed cost stabilization problem. A sufficient condition for guaranteed cost consensus is given in terms of linear matrix inequalities (LMIs), based on a refined time-dependent Lyapunov functional analysis. Reduced-order protocol design methodologies are proposed, with further discussions on determining sub-optimal protocol gain and enlarging allowable sampling interval bound made as a complement. Simulation results illustrate the effectiveness of the theoretical results.

New synchronization criteria for complex delayed dynamical networks with sampled-data feedback control

This paper investigates the synchronization problem for a class of complex delayed dynamical networks (CDDNs) by using sampled-data feedback control. First, an augmented Lyapunov-Krasovskii function (LKF) is constructed, which contains two new triple integral terms to reduce the conservativeness. Second, improved synchronization criteria are proposed by combining reciprocally convex technique with a novel class of integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. Third, the desired sampled-data controllers can be achieved by solving a set of linear matrix inequalities (LMIs). Finally, three numerical simulation examples are presented to demonstrate the effectiveness and advantages of the proposed results.