In this paper, we introduce an innovative generalized Lyapunov theorem and a novel bounded real lemma designed for continuous-time linear singular systems with Caputo fractional derivative of order $\alpha $ , with the constraint $1 \leq {\alpha }\lt 2$ . We initially present a condition that is both necessary and sufficient for establishing the admissibility of singular fractional-order systems (SFOSs). This condition is articulated through strict linear matrix inequalities (LMIs). Following this, we demonstrate that a SFOS satisfies ${H_{\infty }}-$ norm requirement if and only if two strict LMIs are feasible. The key advantage of the presented LMI conditions is that only one matrix variable needs to be solved. Ultimately, this paper concludes by presenting illustrative examples that highlight the practical effectiveness of our theoretical findings.

The strategy of observer‐based nonfragile control and fault‐detection over finite‐time horizon has been examined for a class of uncertain switched nonlinear networked control systems (NNCSs) contingent with time varying delays inferred by the networks from sensor to controller and controller to actuator. Also, in this study, an observer‐based fault detection control has been designed for the NNCSs. By making use of fault detection control as residual generator, the conveyed fault detection problem is then transformed into attenuation problem. By employing multiple Lyapunov function and average dwell time (ADT) approach, sufficient conditions in terms of linear matrix inequalities (LMIs) ensures the finite‐time boundedness (FTB) criterion of the resulting switched NNCSs with a prescribed disturbance attenuation. Subsequently, the preferred LMIs constraints realizes the controller and observer gains. Finally, two numerical examples are proffered to showcase the efficacity of the proposed technique.

This paper utilises the disturbance rejection technique to address a category of Bouc-Wen (BW) hysteresis systems, employing the equivalent input disturbance (EID) method. A novel output feedback hysteresis state estimator is formulated to estimate the virtual hysteresis state. Additionally, a constructed EID estimator is utilised to estimate the impact of the exogenous disturbances on the proposed system. It is necessary to construct a novel control law that integrates the EID estimation to provide adequate disturbance rejection performance. Utilising both a Lyapunov approach and the EID technique, we derive a collection of adequate conditions to guarantee the stability of the BW hysteresis systems. The representation of these conditions takes the form of linear matrix inequalities (LMIs). Finally, a numerical example illustrating the efficacy and practicality of the devised control strategy is used in conjunction with a real-world application called a piezo-positioning mechanical system.

In this paper, a modulated dual-voltage-vector model-free predictive current control with online duty cycle calculation is proposed and applied to drive a synchronous reluctance motor. The dual-voltage-vector modulation scheme reduces the current ripples and errors in the single-voltage-vector method. The proposed method reduces the predictive current controller's calculation time by first setting the initial value of the duty cycle to a constant. Then, an optimal switching mode can be selected by minimizing a cost function. Next, the required duty cycle can be calculated directly by the proposed method without any differential calculations instead of its initial value. The proposed method can effectively track the stator current, reducing the maximum average current error by 34.8% compared to the conventional single-voltage-vector scheme. Finally, the correctness and feasibility of the modulated model-free predictive current controller with the online duty cycle calculation proposed in this article are verified by the experimental results using Texas Instruments microcontroller TMS320F28379D.

This research examines the issue of state-constrained stabilizing controllers for Bouc-Wen hysteresis control systems with all hysteresis parameters being unknown. We develop a novel hysteresis estimator for estimating the virtual hysteresis state. Employing the $L_{2}$ -gain control approach effectively mitigates the impact of estimation errors on the system. With barrier functions, even when the hysteresis parameters are unknown, we can formulate state-constrained stabilizing controllers using solutions to linear matrix inequalities. Ultimately, we showcase the efficacy and practicality of this control strategy with the help of a numerical example.

This letter investigates the design of state-constrained stabilizing controllers for hysteresis control systems with the classical Bouc-Wen model. A novel hysteresis estimator is developed to estimate the virtual hysteresis state. The effect of the estimation error on the system is suppressed by using the $L_{2}$ –gain control approach. We use a barrier function to prevent violation of state constraints. With the help of barrier functions, state-constrained stabilizing controllers can be built by solving linear matrix inequalities. Sufficient conditions for the existence of state-constrained controllers are derived. Finally, a numerical example demonstrates the effectiveness and applicability of the developed control strategy.

This paper employs the disturbance rejection technique for a class of switched nonlinear networked control systems (SNNCSs) with an observer-based event-triggered scheme. To estimate the influence of exogenous disturbances on the proposed system, the equivalent input disturbance (EID) technique is employed to construct an EID estimator. To provide adequate disturbance rejection performance, a new control law is built that includes the EID estimation. Furthermore, to preserve communication resources, an event-based mechanism for control signal transmission is devised and implemented. The primary goal of this work is to provide an observer-based event-triggered disturbance rejection controller that ensures the resulting closed-loop form of the examined systems is exponentially stable. Specifically, by employing a Lyapunov–Krasovskii approach, a new set of sufficient conditions in the form of linear matrix inequalities (LMIs) is derived, ensuring the exponential stabilization criteria are met. Eventually, a numerical example is used to demonstrate the efficacy and practicality of the proposed control mechanism.

This study examines the finite-time event-triggered control (ETC) problem for nonlinear switched cyber-physical systems (NSCPSs) by using an asynchronous switching strategy. An ETC scheme, along with a measurement size reduction technique, has been implemented to decrease network communication burden and redeem network resources. Data quantization is also another efficient method for reducing the amount of transmitted data via networks. Meanwhile, asynchronous phenomena among ETC instants are studied, which is much more realistic and difficult in the system under consideration. The prime intent of this research is to enhance the asynchronous event-triggered control (AETC) technique to guarantee the resulting closed-loop NSCPS is finite-time bounded (FTB) and prespecified mixed $H_{\infty} $ and passive performance index $\gamma $ in the finite-time horizon. A novel set of required conditions in the form of linear matrix inequalities (LMIs) is enhanced using the Lyapunov-Krasovskii functional (LKF) theory, ensuring that the FTB criterion is met. Furthermore, the gains are acquired by solving a group of LMIs. Ultimately, a numerical illustration is provided, showcasing the efficaciousness and practicality of the developed control strategy through a real-world application known as the vertical take-off and landing helicopter model (VTOLHM).

This study inspects the issue of robust reliable sampled data control (SDC) for a class of Takagi-Sugeno (TS) fuzzy CE151 Helicopter systems with time-varying delays and linear fractional uncertainties. Specifically, both the variation range and the distribution probability of the time delay are considered in the control input. The essential aspect of the suggested results in this study is that the time variable delay in the control input is dependent not only on the bound but also on the distribution probability of the time delay. The prime intent of this study is to enhance a state feedback reliable sampled-data controller. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and employing a linear matrix inequalities (LMIs) approach, a new set of delay-dependent necessary conditions is obtained to ensure the asymptotic stabilisation of a TS fuzzy CE151 Helicopter system with a prescribed mixed H∞ and passivity (MH∞P) performance index. The acquired results are expressed as LMIs, which are easily addressed using standard optimization algorithms. In addition, an exemplary scenario based on the CE151 helicopter model is presented to demonstrate the less conservative nature of the obtained results as well as the application of the recommended unique design approaches.

SummaryAn event‐triggered nonfragile distributed H∞ control problem is considered in this article for a class of uncertain nonlinear networked control systems over sensor networks with random communication packet dropouts and redundant channels. Redundant channel transmission is utilized to model the communication measurement and to improve the reliability and quality of the communication data transmission services. In addition, measurement size reduction technique is applied to reduce the energy consumption. An event based transmission scheme is employed to reduce the network burden and energy consumption during the data communication from the sensor to the estimator. With known conditional probability distribution, the random packet losses are modeled as a Bernoulli distributed white sequences. A new set of sufficient conditions is established by using average dwell time approach to obtain the desired observer‐based distributed nonfragile controller with the H∞ performance requirements. Specifically, the explicit form of an observer‐based feedback parameters can be obtained by solving a set of linear matrix inequalities. Finally, to demonstrate the effectiveness of the proposed observer‐based feedback approach, a numerical example is exploited.

In this paper, the finite-time event-triggered and guaranteed non-fragile cost control problem is discussed for a class of uncertain switched nonlinear networked control systems (SNNCS) which involves parameter uncertainties and time-varying transmission delays. The main aim of this work is to synthesize finite-time event-triggered and guaranteed cost non-fragile controller for ensuring the finite-time boundedness of the resulting SNNCS with optimal dissipative performance index. By proposing an appropriate Lyapunov–Krasovskii functional and using the average dwell time technique, a set of new delay-dependent finite-time boundedness conditions is established in terms of linear matrix inequalities to obtain the desired result. The proposed approach unifies the H∞,L2−L∞, passivity and (Q,S,R) - dissipativity performance concept in a single framework. Further, the associated optimization problem is formulated to minimize the guaranteed cost performance bound. To save communication resources, an event-based rule is also introduced and implemented for the control signal transmission. Finally, two numerical examples with simulations are provided to demonstrate the efficiency of the developed control design technique.

This paper investigates the problem of event-triggered observer-based fault detection for a class of uncertain switched nonlinear network control systems (SNNCSs) with random communication packet losses and infinite distributed delay. The main objective of this work is to design an event-triggered state feedback non-fragile H∞ controller such that the resulting closed-loop form of the considered SNNCSs is robustly finite-time bounded and satisfies a prescribed H∞ performance constraint in the finite-time interval. By employing average dwell time approach, the problem of finite-time boundedness and residual H∞ performance analysis is discussed. Specifically, a new set of conditions in the form of LMIs are derived to ensure the finite-time boundedness with the prescribed residual H∞ performance for the relevant closed-loop system. Moreover, the desired observer-based state feedback controller gain matrices and residual weighting matrices can be expressed in an explicit form. Finally, the applicability and effectiveness of the developed results are examined via numerical examples with simulation results.

In this paper, the problem of event-triggered non-fragile state estimator design for discrete-time delayed neural networks (DNNs) is investigated over finite-time span. In consideration of the changes of environment and high sensitivity, external disturbances and/or parameter uncertainties might be involved in estimator parameters of the concerned DNNs. Therefore, it is one of our main objectives to design a non-fragile state estimator subject to the norm bounded gain variation. The sensor nonlinearity is supposed to occur in a random way. In the meanwhile, the event-triggered scheme and energy constraints are adopted in state estimator design for the purpose of energy and resource saving. By using the Lyapunov stability theory and some analytical techniques, sufficient conditions are established to guarantee that the estimation error system is finite-time bounded and meet a prescribed mixed H ∞ and passivity performance constraint. Furthermore, the estimator gains are obtained via solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are exploited to demonstrate the effectiveness of the developed technique.

This paper investigates the problem of robust stabilization for a class of discrete-time Takagi–Sugeno (TS) fuzzy systems via input random delays in control input. The main objective of this paper is to design a state feedback H∞ controller. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust H∞ controller. In particular, the effect of both variation range and distribution probability of the time delay is taken into account in the control input. The key feature of the proposed results in this paper is that the time‐varying delay in the control input not only dependent on the bound but also the distribution probability of the time delay. The obtained results are formulated in terms of LMIs which can be easily solved by using the standard optimization algorithms. Finally, a numerical example with simulation result is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed result.

This article studies the reliable robust stabilization problem for a class of uncertain Takagi–Sugeno (TS) fuzzy systems with time-varying delays. The delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form. By implementing a proper novel Lyapunov functional together with linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions is derived to guarantee the asymptotic stability of TS fuzzy system with a prescribed H∞ performance index. Further, a reliable robust H∞ control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain TS fuzzy system. Further, Schur complement and Jensen's integral inequality are used to simplify the derivation in the main results. The set of sufficient conditions is established using the relationship among the random time-varying delay and its lower and upper bounds, which can be easily solved by MATLAB LMI toolbox. Finally, an illustrative example based on the truck-trailer model is provided to show the effectiveness of the proposed new design technique.

This paper investigates the problem of robust stabilization for a class of discrete-time stochastic neural networks with randomly occurring discrete and distributed time-varying delays. More precisely, the neuron activation functions are assumed to be more general and satisfy sector-like nonlinearities. Moreover, the effects of both variation range and probability distribution of mixed time-delays are taken into consideration in the proposed problem. The main objective of this paper is to design a state feedback reliable H∞ controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop form of considered neural network is robustly asymptotically stable while satisfying a prescribed H∞ performance constraint. Linear matrix inequality approach together with proper construction of Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust reliable H∞ controller. The obtained results are formulated in terms of linear matrix inequalities (LMIs) which can be easily solved by using the MATLAB LMI toolbox. Finally, a numerical example with simulation results is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed results.

This paper considers the issue of state estimation for a class of bidirectional associative memory (BAM) neural networks. More precisely, the BAM model is considered with mixed delays which includes a constant delay in the leakage term, time-varying discrete delay and constant distributed delay. By constructing a novel Lyapunov–Krasovskii functional (LKF) together with free-weighting matrix technique, a new delay dependent sufficient condition is derived to estimate the neuron states through available output measurements such that, for all admissible delay bounds, the resulting estimation error system is globally asymptotically stable. Also it is assumed that the derivative of time delay is not necessarily zero or less than one. Further the derived conditions are formulated in terms of a set of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Finally a numerical example with simulation result is presented to show the effectiveness of the proposed theory. The result reveals that the leakage delays have a destabilizing influence on the system and they cannot be ignored.

This article addresses the issue of robust sampled-data H∞ control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov-Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level γ>0 about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jenson's integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled-data H∞ controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled-data H∞ control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19-29, 2015

This article focuses on the robust state feedback reliable H ∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H ∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.

In this article, we consider the problem of reliable H∞ control for a class of uncertain mechanical systems with input time-varying delay and possible occurrence of actuator faults. In particular, we assume that linear fractional transformation (LFT) uncertainty formulations appear in the mass, damping, and stiffness matrices. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable while satisfying a prescribed H∞ performance constraint. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived in terms of LMIs for the existence of robust reliable H∞ controller. Further, Schur complement and Jenson's integral inequality are used to substantially simplify the derivation in the main results. The obtained results are formulated in terms of LMIs which can be easily verified by the standard numerical softwares. Finally, numerical examples with simulation result are provided to illustrate the applicability and effectiveness of the proposed reliable H∞ control scheme. The numerical results reveal that the proposed theory significantly improves the upper bound of time delays and minimum feasible H∞ performance index over some existing works.