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In this paper, a new fuzzy Functional observer is developed for nonlinear neutral systems. Also, the existence conditions for it are studied. The delay-dependent stability of this observer is guaranteed by the combination of the solution of the Sylvester equation and the Lyapunov–Krasovskii stability approach. The parameters of the studied observer are obtained by solving linear matrix inequalities (LMIs). The performance of the approach developed in this paper is demonstrated at the end of the paper by numerical examples. [ABSTRACT FROM AUTHOR]

In this article, the guaranteed cost control problem for a class of nonlinear networked control systems (NCSs) with dynamic quantization, external bounded disturbance, and data dropout is investigated via the dynamic output feedback. The Takagi–Sugeno (T-S) fuzzy model is used to represent the discrete-time nonlinear system discussed in this paper. Under the dynamic quantization strategy, two quantizers with dynamic parameters are used to quantize the measured output and control input, and the data dropout process is described by introducing the Bernoulli stochastic variable. By using the quadratic boundedness technique, the quadratic stability of the quantized NCS with external disturbance is described. Furthermore, the sufficient condition for the global design approach are proposed, that is, not only the dynamic output feedback controller but parameters of the quantizers are designed synchronously with strict linear matrix inequalities. Eventually, a simulation of nonlinear mass-spring-damper mechanical system is carried out to verify the effectiveness of the provided algorithm. [ABSTRACT FROM AUTHOR]

The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is studied. First, like a normal system, the whole nonlinear system is transformed into a local linear system, and then a large number of linear system theories can be applied to solve related problems. Second, in the observer design of general discrete-time Markov jump systems, only the unknown input in the state equation is usually considered. In this paper, the unknown input is considered in both the state equation and the output equation. The state estimation error system is derived by defining the error. The non-uniform Lyapunov functional is selected to stabilize the estimation error system using the Lyapunov theory. The sufficient conditions for the stability of the system are obtained and transformed into the feasibility problem of linear matrix inequality. The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is solved using MATLAB software. Finally, a numerical example of two rules and two modes is used to verify the effectiveness and feasibility of the proposed unknown input observer. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method. [ABSTRACT FROM AUTHOR]

The robust synchronization of uncertain master–slave Lur'e systems based on time-delayed feedback control is further investigated. A less conservative synchronization stability criterion and a less conservative robust synchronization stability criterion than some recent published references are proposed via Lyapunov stability theory. First, an augmented delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed, where some single integral terms are augmented to the integrand component of a single-integral subfunction. This not only increases some coupling information on some system variables but also increases the coupling information on some necessary variables contained in the inequality lemmas, which can make full use of the inequality lemmas and reduce the conservatism of the synchronization stability criterion. Second, to overcome the nonlinear phenomena in the synchronization criterion, the novel negative definite inequality equivalent transformation lemma is used to transform the nonlinear inequalities to the linear matrix inequalities (LMIs) equivalently, which can be easily solved by the MATLAB LMI-Toolbox. Finally, some common numerical examples are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper introduces an H ∞ robust constrained event-triggered fuzzy controller for discrete-time nonlinear systems in the presence of system parameter uncertainties, the parameter uncertainties of the output matrices and the disturbances, simultaneously. To reduce the communication resources and improve the robust performance, the event-triggered mechanism is incorporated with the H ∞ robust fuzzy controller design. Moreover, by employing the fuzzy modeling of the actuator saturation and a nonquadratic Lyapunov function (NQLF), the ultimate bounded stability (UBS) of the closed-loop system is guaranteed subject to the amplitude limitations of the control signal. This means, a new linear matrix inequality (LMI) problem is derived to ensure the robustness and constraints in an offline scheme based on the event-triggered strategy. Besides, to meet the practical problem to further improve the controlled system performance, the control input rate constraint is also considered and a new LMI condition is provided with no online computational burden. Therefore, the computational burden of the proposed controller is greatly reduced with less conservatism. Two simulation examples including a numerical dynamic system and a truck–trailer system are employed to illustrate the less conservatism and computational complexity of the proposed method compared with the existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, we consider the finite-time boundedness (FTB) and finite-time stabilization boundedness (FTSB) problems for a class of nonlinear interconnected systems with Atangana–Baleanu–Caputo (ABC) fractional derivative. By employing the FTB theory and some properties of ABC fractional derivative, and some basic mathematical transformations, we derive new conditions for the FTB and FTSB problems of ABC fractional-order nonlinear interconnected systems. These conditions are formed in linear matrix inequalities (LMIs), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, two numerical examples with simulations are provided to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This study introduces a novel H ∞ optimal constrained integral sliding mode control (OCISMC) for nonlinear systems due to the matched/unmatched external disturbances based on Takagi–Sugeno (TS) fuzzy models. Based on the Lyapunov function, the appropriate conditions are provided to reach the sliding mode from any initial condition and robustness against the matched disturbances is guaranteed. The optimal nominal part of the proposed OCISMC is designed based on an online optimization problem. To reach robustness against the unmatched disturbances and constrained controller, the H ∞ performance and the limitations of the control signal are included in the design procedure of the suggested OCISMC. Furthermore, by considering a non-quadratic Lyapunov function (NQLF), a new linear matrix inequality problem with less conservatism is derived. Finally, two examples are simulated and compared with the existing works to illustrate the capability of the proposed OCISMC. [ABSTRACT FROM AUTHOR]

The design of dynamic H' 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 H' 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. [ABSTRACT FROM AUTHOR]

This paper presents fuzzy tracking control strategies for classes of linear and bilinear Takagi-Sugeno Fuzzy System with Uncertainties and Disturbances (T-S FSUD). For both classes, the Lyapunov direct approach and the parallel distributed compensation concept are used to design nonfragile H ∞ tracking controllers, which ensure the robust asymptotic stability of augmented systems despite the presence of parameter uncertainties, external disturbances, and controllers fragility. Besides that, based on the Schur complement, the separation lemma, and through some variable transformations, sufficient stability conditions of each augmented T-S FSUD are established and formulated in terms of linear matrix inequalities. Finally, numerical simulations are carried out to demonstrate the validity and the applicability of designed control schemes on tracking control of an inverted pendulum and a nonlinear mechanical system. [ABSTRACT FROM AUTHOR]

This paper proposes the adaptive quantized controller design for the synchronization of a class of fractional-order nonlinear systems satisfying incremental quadratic constraints governed by an incremental multiplier matrix. The incremental quadratic constraints can describe many commonly encountered nonlinearities in existing literature. The adaptive quantized controller are designed and formulated in terms of matrix inequalities to make the error system asymptotically stable. Meanwhile, the sufficient conditions can be obtained via solving linear matrix inequalities. Moreover, an algorithm is presented to illustrate the steps of designing adaptive quantized controllers. Finally, examples about fractional-order Lorenz chaotic system and fractional-order Bloch system are provided to illustrate the effectiveness of the designed controller. [ABSTRACT FROM AUTHOR]

Considering the complexity and universality of nonlinearity in control systems, it is of great significance to investigate the robust proportional-derivative type (PD-type) iterative learning control (ILC) design for repetitive nonlinear systems in the Takagi–Sugeno (T–S) forms, Different from existing ILC laws, the proposed ones are designed in the finite-frequency domain. The nonlinear systems are described by Roesser-type two-dimensional (2D) uncertain T–S fuzzy models with non-repetitive disturbances. The main contribution of this article is that the novel fuzzy ILC method is proposed by exploiting the 2D linear systems theory. Further to this, the proposed design guarantees the robust asymptotic stability and finite-frequency 2D H ∞ performance of the resulting fuzzy systems, and the controller gains are obtained by solving a set of linear matrix inequality (LMI) constraints. Through the simulation of a nonlinear single-link rigid robot system, our major findings are that the proposed fuzzy control algorithm can lead to steady-state tracking performance and good robustness against non-repetitive disturbances and uncertainties, and the PD-type ILC performs significantly better than the P-type ILC, the former can efficiently improve the control effect. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered consensus problem of second-order nonlinear multi-agent systems subject to denial-of-service (DoS) attacks, which make the communication network unable to provide normal services. Considering a general class of DoS attack with limited duration, a novel distributed event-triggered consensus protocol accompanied with first-order hold is adopted to guarantee the globally bounded consensus convergence under directed network topology. Based on the linear matrix inequality approach and Lyapunov stability method, consensus converging properties are analysed and sufficient criteria are obtained. Furthermore, Zeno-free triggering of our proposed protocol is demonstrated. Finally, a numerical simulation is given to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the preview tracking control problem for Lipschitz nonlinear system, where future reference signals over a finite horizon can be previewed. First, an augmented error system including previewed information is constructed, which transforms a preview tracking control problem into a regulation problem. Furthermore, sufficient conditions on polytopic nonlinear systems, which guarantee the corresponding closed-loop system to be asymptotically stable, are derived by employing parameter-dependent Lyapunov function. A linear matrix inequality approach for designing preview controllers in state feedback and output feedback settings is presented. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the H ∞ control problem for Lipschitz nonlinear systems in the finite-frequency domain. Both parameter uncertainties and external disturbances are considered. In contrast to existing full-frequency methods, the proposed approach takes into account of the frequency information of disturbances during the design proceeding. Sufficient analysis conditions for the closed-loop system are firstly derived. Then, synthesis conditions are formulated in terms of linear matrix inequalities (LMIs). In fact, the control gain is designed to attenuate the influence of disturbances in different frequency ranges (low, middle and high). Finally, the model of the Chua circuit is used to validate the effectiveness of the proposed finite-frequency approach and to prove its superiority compared to the full-frequency counterpart. [ABSTRACT FROM AUTHOR]