Search results

In this paper, a novel Lyapunov–Krasovskii stable fuzzy proportional-integral-derivative (PID) (FPID) controller is introduced for load frequency control of a time-delayed micro-grid (MG) system that benefits from a fuel cell unit, wind turbine generator and plug-in electric vehicles.

Using the Lyapunov–Krasovskii theorem, the adaptation laws for the consequent parameters and output scaling factors of the FPID controller are developed in such a way that an upper limit (the maximum permissible value) for time delay is introduced for the stability of the closed-loop MG system. In this way, there is a stable FPID controller, the adaptive parameters of which are bounded. In the obtained adaptation laws and the way of stability analyses, there is no need to approximate the nonlinear model of the controlled system, which makes the implementation process of the proposed adaptive FPID controller much simpler.

It has been shown that for a different amount of time delay and intermittent resources/loads, the proposed adaptive FPID controller is able to enforce the frequency deviations to zero with better performance and a less amount of energy. In the proposed FPID controller, the increase in the amount of time delay leads to a small increase in the amount of overshoot/undershoot and settling time values, which indicate that the proposed controller is robust to the time delay changes.

Although the designed FPID controllers in the literature are very efficient in being applied to the uncertain and nonlinear systems, they suffer from stability problems. In this paper, the stability of the FPID controller has been examined in applying to the frequency control of a nonlinear input-delayed MG system. Based on the Lyapunov–Krasovskii theorem and using rigorous mathematical analyses, the stability conditions and the adaptation laws for the parameters of the FPID controller have been obtained in the presence of input delay and nonlinearities of the MG system.

This paper is concerned with non-fragile robust H_∞ control problems for nonlinear networked control systems (NCSs) with time-varying delay and unknown actuator failures. The paper aims to discuss these issues.

The system parameters are allowed to have time-varying uncertainties and the actuator faults are unknown but whose upper and lower bounds are known. By using some lemmas, uncertainties can be replaces with the known values. By taking the exogenous disturbance and network transmission delay into consideration, a delay nonlinear system model is constructed.

Based on Lyapunov stability theory, linear matrix inequalities (LMIs) and free weighting matrix methods, the sufficient conditions for the existence of the non-fragile robust H_∞ controller gain are derived and which can obtained by solving the LMIs. Finally, a numerical example is provided to illustrate the effectiveness of the proposed methods.

The introduced approach is interesting for NCSs with time-varying delay and unknown actuator failures.

This paper aims to use a new design approach based on a Lagrange mean value theorem for the stabilization of multivariable input‐delayed system by linear controller.

The delay‐dependent asymptotical stability conditions are derived by using augmented Lyapunov‐Krasovskii functionals and formulated in terms of conventional Lyapunov matrix equations and some simple matrix inequalities. Proposed design approach is extended to robust stabilization of multi‐variable input‐delayed systems with unmatched parameter uncertainties. The maximum upper bound of delay size is computed by using a simple optimization algorithm.

A liquid monopropellant rocket motor with a pressure feeding system is considered as a numerical design example. Design example shows the effectiveness of the proposed design approach.

The proposed approach can be used in the analysis and design of the uncertain multivariable time‐delay systems.

The paper has a great potential in the stability analysis of time‐delay systems and design of time‐delay controllers and may openup a new direction in this area.

The purpose of this paper is to obtain the criteria of p‐moment exponential robust stability for a class of grey neutral stochastic delay systems.

By constructing a Lyapunov‐Krasovskii functional and employing the decomposition technique of continuous matrix‐covered sets of grey matrix and using three key inequalities, the paper investigates the p‐moment exponential robust stability for a class of grey neutral stochastic delay systems. A numeric example is given to demonstrate the effectiveness of the criteria presented in the paper.

The results not only can be used to judge the p‐moment exponential robust stability of the systems researched in the paper, but also can be applied in the stability analysis of grey non‐neutral stochastic systems.

The method exposed in the paper can be used in the analysis and designation of practical stochastic control systems.

The paper succeeds in obtaining the criteria of p‐moment exponential robust stability for grey neutral stochastic delay systems by constructing a Lyapunov‐Krasovskii functional and employing the decomposition technique of continuous matrix‐covered sets of grey matrix and using three key inequalities.

As a class of stochastic hybrid systems, Markovian jump systems have been extensively studied in the past decades. In light of some results obtained on this topic. The purpose of this paper is to investigate the stability problems for delayed Markovian jump systems.

The time‐varying‐delays considered in this paper are switched synchronously with system mode. Based on stochastic Lyapunov theory, the delay‐dependent stability conditions are developed by using some linear matrix inequality techniques. To obtain better stability criteria, the different Lyapunov‐Krasovskii functional is chosen and an important inequality is introduced.

Numerical examples show that the resulting criteria in this paper have advantages over some previous ones in that they involve fewer matrix variables, but have less conservatism. Furthermore, they only involve the matrix variables appeared in the Lyapunov functional. Therefore, there are no additional matrix variables coupled with the system matrices, which will be easier to investigate the synthesis problems for the underlying systems and save much computation.

The introduced approach is more efficient to investigate the stability for Markovian jump systems with mode‐dependent time‐varying‐delays.

The purpose of this paper is to investigate the neural-network-based containment control of multi-agent systems with unknown nonlinear dynamics. Moreover, communication constraints are taken into account to reflect more realistic communication networks.

Based on the approximation property of the radial basis function neural networks, the control protocol for each agent is designed, where all the information is exchanged in the form of sampled data instead of ideal continuous-time communications.

By utilizing the Lyapunov stability theory and the Lyapunov–Krasovskii functional approach, sufficient conditions are developed to guarantee that all the followers can converge to the convex hull spanned by the stationary leaders.

As ideal continuous-time communications of the multi-agent systems are very difficult or even unavailable to achieve, the neural-network-based containment control of nonlinear multi-agent systems is solved under communication constraints. More precisely, sampled-data information is exchanged, which is more applicable and practical in the real-world applications.

The purpose of this paper is to develop a method for the existence, uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays, continuous distributed delays and a kind of discontinuous activation functions.

Based on the Leray–Schauder alternative theorem and chain rule, by using a novel integral inequality dealing with monotone non-decreasing function, the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.

It turns out that the authors’ delay-dependent sufficient condition can be formed in terms of linear matrix inequalities conditions. Two examples show the effectiveness of the obtained results.

The novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem, chain rule and a novel integral inequality on monotone non-decreasing function.

The purpose of this paper is to propose a guaranteed cost control design procedure for model-based cyber–physical assembly (CPA) systems. To reflect the cyber–physical environment, the network-induced delays and disturbances are introduced in the mathematical model.

Based on the linear matrix inequality approach, the guaranteed cost controller is designed such that the guaranteed cost can be satisfied and the corresponding convex optimization algorithm is provided. Moreover, H-infinity theory is used to deal with the disturbance with the given H-infinity attenuation level.

By constructing appropriate Lyapunov–Krasovskii functionals, delay-dependent sufficient conditions are established in terms of linear matrix inequalities and the controller design procedure is given.

A simplified CPA model is given based on which the designed controller can allow us to control the closed-loop CPA systems with the guaranteed cost.

The power framework has become a vital part in the day-to-day life and exhibits a rapid development in this current era. Due to the fact of huge power utilization, the power frameworks fall under several power transmission-related concerns. Precisely, frequency deviation has generated a huge impact during power transmission; this in turn highly reduces the power system stability as well as reliability too.

To boost the system’s efficacy, this study proposes a neoteric closed loop feedback controller in which a control algorithm named correlative-elemental-curvature algorithm is introduced with a constant threshold.

With the aim of mitigating frequency deviation, a stability analysis technique called Retrofit Lyapunov’s method is deployed in the controller. This would simultaneously reduce the load disturbances along with tie-line synchronization issues faced with the prior controllers. Optimization is carried out with the aid of duelist optimization algorithm, which tunes the controller parameters thereby mitigating the complexities while designing a loop feedback controller power framework.

The efficacy of the proposed work is assessed with the aid of metrics, such as integral absolute error, accuracy and settling time. Thus, the proposed work enhances the system reliability as well as the stability by mitigating the frequency deviation related issues and guarantees reliable power transmission.

This paper aims to address the robust controller design problem for a class of fuzzy C-means clustering algorithm that is robust against both the plant parameter perturbations and controller gain variations. Based on Takagi–Sugeno (T-S) fuzzy model description, the stability and control problems of nonlinear systems are studied.

A recently proposed integral inequality is selected based on the free-weight matrix, and the less conservative stability criterion is given in the form of linear matrix inequalities (LMIs).

Under the premise that the controller and the system share the same, the method does not require the number of membership functions and rules.

Furthermore, the modified controller in a large-scale nonlinear system is utilized as a stability criterion for a closed-loop T-S fuzzy system obtained by LMI, and is rearranged by a machine learning membership function.

The closed-loop controller criterion is derived by energy functions to guarantee the stability of systems. Finally, an example is given to demonstrate the results.