Robust reliable dissipative control of nonlinear networked control systems

This article focuses on the robust reliable dissipative control issue for a class of switched discrete‐time nonlinear networked control systems with external energy bounded disturbances. In particular, nonlinearities are modeled in a probabilistic way according to Bernoulli distributed white sequence with known conditional probability. A Lyapunov–Krasovskii functional is proposed based on which sufficient conditions for the existence of the reliable dissipative controller are derived in terms of linear matrix inequalities (LMIs) which ensures exponentially stability as well as dissipative performance of the resulting closed‐loop system. The explicit expression of the desired controller gains can be obtained by solving the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed design strategy. © 2016 Wiley Periodicals, Inc. Complexity 21: 427–437, 2016     

Dissipative analysis for discrete‐time systems via fault‐tolerant control against actuator failures

This article investigates the problem of robust dissipative fault‐tolerant control for discrete‐time systems with actuator failures. Based on the Lyapunov technique and linear matrix inequality (LMI) approach, a set of delay‐dependent sufficient conditions is developed for achieving the required result. A design scheme for the state‐feedback reliable dissipative controller is established in terms LMIs which can guarantee the asymptotic stability and dissipativity of the resulting closed‐loop system with actuator failures. In addition, the proposed controller not only stabilize the fault‐free system but also to guarantee an acceptable performance of the faulty system. Also as special cases, robust H_∞ control, passivity control, and mixed H_∞ and passivity control with the prescribed performances under given constraints can be obtained for the considered systems. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault‐tolerant control technique. © 2016 Wiley Periodicals, Inc. Complexity 21: 579–592, 2016     

Robust reliable sampled‐data H∞ control for uncertain stochastic systems with random delay

In this article, the problem of robust reliable sampled‐data control for a class of uncertain nonlinear stochastic system with random delay control input against actuator failures has been studied. In the considered system, the parameter uncertainty satisfies the norm bounded condition and the involved time delay in control input are assumed to be randomly time‐varying which is modeled by introducing Bernoulli distributed sequences. By constructing a novel Lyapunov–Krasovskii functional involving with the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for ensuring the robust asymptotic stability of the uncertain nonlinear stochastic system with random delay and disturbance attenuation level about its equilibrium point for all possible actuator failures. In particular, Schur complement together with Jenson's integral inequality is utilized to substantially simplify the derivation in the main results. The derived analytic results are applied to design robust reliable sampled‐data controller for hanging crane structure model and simulation results are provided to demonstrate the effectiveness of the proposed control law. © 2014 Wiley Periodicals, Inc. Complexity 21: 42–58, 2015     

Fault‐tolerant sampled‐data mixed ℋ∞ and passivity control of stochastic systems and its application

This article addresses the problem of fault‐tolerant sampled‐data mixed and passivity control for a class of stochastic system with actuator failures, where the plant is modeled as a continuous‐time one and the control inputs are implemented as discrete‐time signals. Sufficient conditions for the reliable sampled‐data mixed and passivity performance control law is established for the considered systems by constructing an appropriate Lyapunov–Krasovskii functional together with the Newton–Leibniz formula and free‐weighting matrix technique. More precisely, linear matrix inequality based sampled‐data methodology is employed to design the mixed and passivity formation controller to reject the impact of the formation changes being treated as disturbances. Simulation studies are performed based on the flight control model to verify the stability, performance, and effectiveness of the proposed design strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 420–429, 2016     

Static output‐feedback control for interval type‐2 discrete‐time fuzzy systems

This article investigates the problem of reliable mixed control for discrete‐time interval type‐2 (IT2) fuzzy model‐based systems via static output‐feedback (SOF) control method. The number of fuzzy rules and the membership functions for the SOF controller are different from those for the plant. A sufficient criterion of reliable stability with mixed performance is derived for the closed‐loop system with sensor failure. The SOF controller is designed for two different cases (known sensor failure case and unknown sensor failure case) to guarantee the reliable stability with mixed performance. Moreover, novel criteria are presented to obtain the optical performance for the closed‐loop system. Finally, an example is used to verify the effectiveness of the proposed design scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 74–88, 2016     

A delay decomposition approach for robust dissipativity and passivity analysis of neutral‐type neural networks with leakage time‐varying delay

This article presents the robust dissipativity and passivity analysis of neutral‐type neural networks with leakage time‐varying delay via delay decomposition approach. Using delay decomposition technique, new delay‐dependent criteria ensuring the considered system to be ‐γ dissipative are established in terms of strict linear matrix inequalities. A new Lyapunov–Krasovskii functional is constructed by dividing the discrete and neutral delay intervals into m and l segments, respectively, and choosing different Lyapunov functionals to different segments. Further, the dissipativity behaviors of neural networks which are affected due to the sensitiveness of the time delay in the leakage term have been taken into account. Finally, numerical examples are provided to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 248–264, 2016     

Quantized control for polynomial fuzzy discrete‐time systems

This article investigates the control problem for polynomial fuzzy discrete‐time systems. Signal quantization is considered in this article. To deal with this issue, a logarithmic quantizer is adopted to quantize the control signal. First, a novel method is first proposed to model polynomial fuzzy discrete‐time systems and handle the quantized control problem of the systems. Second, based on Lyapunov‐stability theory, sufficient conditions are obtained in terms of sum of squares to guarantee the asymptotical stability of the systems and satisfy a performance. Finally, a simulation example is given to illustrate the effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 325–332, 2015     

Positioning control for a linear actuator with nonlinear friction and input saturation using output‐feedback control

This article deals with the positioning control problem via the output feedback scheme for a linear actuator with nonlinear disturbances. In this study, the proposed controller accounts for not only the nonlinear friction, force ripple, and external disturbance but also the input saturation problem. In detail, the energy consumption for conquering friction and disturbance rejection is estimated and used as compensation based on the hybrid controller including and sliding‐mode‐based adaptive algorithms, which ensures the tracking performance and robustness of electromechanical servo system. Moreover, to confront the input saturation, a saturation observer and an anti‐windup controller are designed. The global robustness of the controller is guaranteed by an output feedback robust law. Theoretically, the designed controller can guarantee a favorable tracking performance in the presence of various disturbance forces and input saturation, which is essential for high accuracy motion plant in industrial application. The simulation results verify the robustness and effectiveness for the motion system with the proposed control strategy under various operation conditions. © 2016 Wiley Periodicals, Inc. Complexity 21: 191–200, 2016     

Robust dissipativity and passivity analysis for discrete‐time stochastic neural networks with time‐varying delay

In this article, we consider the problem of robust dissipativity and passivity analysis for a class of general discrete‐time recurrent neural networks (NNs) with time‐varying delays. The NN under consideration is subject to time‐varying and norm bounded parameter uncertainties. By the latest free‐weighting matrix method, an appropriate Lyapunov–Krasovskii functional and using stochastic analysis technique a sufficient condition is established to ensure that the NNs under consideration is strictly ‐dissipative. The derived conditions are presented in terms of linear matrix inequalities. Numerical examples and its simulations are given to demonstrate the effectiveness of the results. © 2014 Wiley Periodicals, Inc. Complexity 21: 47–58, 2016     

Nonfragile H∞ filtering for wireless‐networked systems with energy constraint

This article is concerned with the nonfragile filtering for wireless‐networked systems with energy constraint. To achieve the energy‐efficient goal, the local measurement is first sampled by nonuniform sampling, then we only choose one measurement to transmit it to the remote filter. In the filter design, the random occurring filter gain variation problem is taken into account. A new stochastic switched system model is presented to capture the nonuniform sampling, the measurement size reduction, and the random filter gain phenomena. Based on the switched system approach, stochastic system analysis, and Lyapunov stability theory, a sufficient condition is presented such that the filtering error system is exponentially stable in the mean‐square sense and a prescribed performance level is also guaranteed. The effectiveness of the proposed new method is illustrated by a simulation example. © 2015 Wiley Periodicals, Inc. Complexity 21: 79–89, 2016     

Robust ℋ∞ tracking control for uncertain Markovian jumping systems with interval time‐varying delay

In this article, the problem of robust tracking control for a class of uncertain Markovian jump systems with interval time‐varying delay is investigated. Based on an augmented Lyapunov–Krasovskii functional with triple integral term, partitioning the delay's lower bound and reciprocally convex approach, delay‐dependent conditions for the existence of desired controller are achieved. Meanwhile, stability criteria for delayed Markovian jump systems are also provided with less conservativeness and less matrix variables than some recent results. Finally, two simulation examples are given to illustrate the effectiveness of the proposed design method. © 2014 Wiley Periodicals, Inc. Complexity 21: 355–366, 2015     

Decentralized Piecewise Fuzzy Output Feedback Control for Large‐Scale Nonlinear Systems with Time‐Varying Delay

This article addresses the decentralized output feedback control for discrete‐time large‐scale nonlinear systems. The considered large‐scale system contains several subsystems with nonlinear interconnection and time‐varying delay, and Takagi–Sugeno model is used to represent each nonlinear subsystem. We aim at designing a decentralized piecewise fuzzy memory dynamic‐output‐feedback (DOF) controller that guarantees the stabilization and performance of the resulting closed‐loop control system. First, we propose a model transformation that reformulates the problem of decentralized output feedback control into the stability analysis with input–output form. Then, we introduce a piecewise Lyapunov–Krasovskii functional, where all Lyapunov matrices are not necessarily positive definite. By combining with the scaled small gain theorem, the less conservative solution to the problem of decentralized piecewise fuzzy memory DOF controller design for the considered system is derived in terms of linear matrix inequalities. The advantage of the proposed method is finally validated using two numerical examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 268–288, 2016     

Robust sampled‐data H∞ control for mechanical systems

This article addresses the issue of robust sampled‐data 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 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 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 control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19–29, 2015     

Fault‐tolerant mixed /passive synchronization for delayed chaotic neural networks with sampled‐data control

This article is concerned with the fault‐tolerant mixed /passive synchronization problem for chaotic neural networks by sampled‐data control scheme. The objective is focused on the design of a reliable controller such that the mixed /passivity performance level of the resulting synchronization error system is ensured in the presence of actuator failures. A time‐dependent Lyapunov functional and an improved reciprocally convex approach combined with a novel integral inequality are applied to optimize the availability of the information on the actual sampling pattern. Then, some sufficient conditions of mixed /passivity performance analysis for the synchronization error systems are derived. A desired reliable sampled‐data controller is designed by solving the optimization problems. Finally, to demonstrate the effectiveness of the proposed method, a practical chaotic neural networks is provided. © 2015 Wiley Periodicals, Inc. Complexity 21: 246–259, 2016     

Robust stability results for nonlinear Markovian jump systems with mode‐dependent time‐varying delays and randomly occurring uncertainties

This article is concerned with the robust stability analysis for Markovian jump systems with mode‐dependent time‐varying delays and randomly occurring uncertainties. Sufficient delay‐dependent stability results are derived with the help of stability theory and linear matrix inequality technique using direct delay‐decomposition approach. Here, the delay interval is decomposed into two subintervals using the tuning parameter η such that , and the sufficient stability conditions are derived for each subintervals. Further, the parameter uncertainties are assumed to be occurring in a random manner. Numerical examples are given to validate the derived theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 50–60, 2016     

synchronization of coupled reaction‐diffusion neural networks with mixed delays

The reaction‐diffusion neural network is often described by semilinear diffusion partial differential equation (PDE). This article focuses on the asymptotical synchronization and synchronization for coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. First, using the Lyapunov–Krasoviskii functional scheme, the sufficient condition is obtained for the asymptotical synchronization of coupled semilinear diffusion PDEs with mixed time‐delays and this condition is represented by linear matrix inequalities (LMIs), which is easy to be solved. Then the robust synchronization is considered in temporal‐spatial domain for the coupled semilinear diffusion PDEs with mixed delays and external disturbances. In terms of the technique of completing squares, the sufficient condition is obtained for the robust synchronization. Finally, a numerical example of coupled semilinear diffusion PDEs with mixed time‐delays is given to illustrate the correctness of the obtained results. © 2016 Wiley Periodicals, Inc. Complexity 21: 42–53, 2016     

Finite‐time l2 − l∞ synchronization for discrete‐time nonlinear chaotic systems via information‐constrained delayed feedback

This article is concerned with the problem of finite‐time synchronization control for a class of discrete‐time nonlinear chaotic systems under unreliable communication links. Our aim is to design a delayed feedback controller such that the resulting synchronization error system is stochastically finite‐time bounded with a guaranteed performance level over a finite time interval. Some sufficient conditions for the solvability of the above problem are established. A delayed feedback control scheme involving constrained information about the past state is presented. Finally, the Fold chaotic system is used to demonstrate the effectiveness of our proposed approach. © 2014 Wiley Periodicals, Inc. Complexity 21: 138–146, 2015     

H∞ stochastic synchronization for master–slave semi‐Markovian switching system via sliding mode control

In this article, synchronization problem of master–slave system with phase‐type semi‐Markovian switching is investigated via sliding mode control scheme. By utilizing a supplementary variable technique and a plant transformation, the master–slave semi‐Markovian switching system can be equivalently expressed as its associated Markovian switching system. Then an integral sliding surface is constructed to guarantee stochastic synchronization of master–slave semi‐Markovian switching system, and the suitable controller is synthesized to ensure that the trajectory of the closed‐loop error system can be driven onto the prescribed sliding mode surface. Finally, numerical simulations are presented to show the effectiveness of the proposed sliding‐mode design scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 430–441, 2016     

Extremal t‐apex trees with respect to matching energy

The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. For any integer t≥1, a graph G is called t‐apex tree if there exists a t‐set such that G ? X is a tree, while for any with , G ? Y is not a tree. Let be the set of t‐apex trees of order n. In this article, we determine the extremal graphs from with minimal and maximal matching energies, respectively. Moreover, as an application, the extremal cacti of order n and with s cycles have been completely characterized at which the minimal matching energy are attained. © 2015 Wiley Periodicals, Inc. Complexity 21: 238–247, 2016     

Short communication on the discrete deffuant and alternative models in one dimension

The discrete Deffuant model and its alternatives is a family of stochastic spatial models for the dynamics of binary opinions on f issues. Another parameter is also incorporated that prevents interaction between two agents whenever their opinion profiles are at a Hamming distance greater than the confidence threshold θ. By numerical simulations, it was conjectured in (Adamopoulos and Scarlatos, Complexity 2012, 17, 43) that one‐dimensional models exhibit a phase transition at a critical value . We report on recent mathematical results on this problem that originates from the community of complex systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 437–439, 2016