Finite‐region stability and finite‐region boundedness for 2D Roesser models

In this paper, we establish finite‐region stability (FRS) and finite‐region boundedness analysis methods to investigate the transient behavior of discrete two‐dimensional Roesser models. First, by building special recursive formulas, a sufficient FRS condition is built via solvable linear matrix inequalities constraints. Next, by designing state feedback controllers, the finite‐region stabilization issue is analyzed for the corresponding two‐dimensional closed‐loop system. Similar to FRS analysis, the finite‐region boundedness problem is addressed for Roesser models with exogenous disturbances and corresponding criteria, and linear matrix inequalities conditions are reported. To conclude the paper, we provide numerical examples to confirm the validity of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

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     

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     

Finite‐time stabilization of complex dynamical networks via optimal control

An optimal control scheme is proposed to stabilize complex networks in finite time. Furthermore, since it is costly and impractical to control a network by applying controllers to all the nodes, an algorithm inspired by Kalmans controllability rank condition is presented for local stabilization by locating pinned components. Numerical examples are provided to illustrate the effectiveness of the proposed method as well as its superiority over a traditional pinning control technique. This work offers a theoretical framework for designing optimal controllers to stabilize networks in finite time with reduced control cost. © 2016 Wiley Periodicals, Inc. Complexity 21: 417–425, 2016     

Relaxed fuzzy observer‐based output feedback control synthesis of discrete‐time nonlinear control systems

This work develops the development of observer‐based output feedback control design of discrete‐time nonlinear systems in the form of Takagi–Sugeno fuzzy model. Lately, previous results have been improved in virtue of a two‐step method. From a technical point of view, it is not flawless and related problems have not been completely resolved. In this study, more advanced two‐steps approach is further developed while the relative sizes among different normalized fuzzy weighting functions are utilized by introducing some additional matrix variables. As a result of the above work, those main defects of the existing method can be redressed and a desired solution in aspect of not only reducing the conservatism but also alleviating the computation complexity is provided for some special cases. Moreover, the effectiveness of the proposed result is shown at length by means of an illustrative example. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–601, 2016     

Dynamic output feedback consensus of continuous‐time networked multiagent systems

This article addresses the dynamic output feedback consensus problem of continuous‐time networked multiagent systems. Both a fixed topology and Markovian switching topologies are considered. The consensus algorithms are on the base of the output information of each agent's itself and its neighbors. Some sufficient conditions for consensus of multiagent systems are obtained in forms of bilinear matrix inequalities. The algorithm based on the homotopy continuation method is given to compute the feasible controller gains. Numerical simulations are given to show the effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 35–42, 2015     

Exponential H∞ synchronization for discrete‐time chaotic neural networks with time delays and stochastic perturbations via output feedback control

This paper investigates the problem of exponential H_∞ synchronization of discrete‐time chaotic neural networks with time delays and stochastic perturbations. First, by using the Lyapunov‐Krasovskii (Lyapunov) functional and output feedback controller, we establish the H_∞ performance of exponential synchronization in the mean square of master‐slave systems, which is analyzed using a matrix inequality approach. Second, the parameters of a desired output feedback controller can be achieved by solving a linear matrix inequality. Finally, 2 simulated examples are presented to show the effectiveness of the theoretical results.     

LMI‐based criterion for the robust guaranteed cost control of uncertain switched neutral systems with time‐varying mixed delays and nonlinear perturbations by dynamic output feedback

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time‐varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay‐dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water‐quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555–578, 2016     

Tracking control of chaotic spinning disks via nonlinear dynamic output feedback with input constraints

In many control engineering applications, it is impossible or expensive to measure all the states of the dynamical system and only the system output is available for controller design. In this study, a new dynamic output feedback control algorithm is proposed to stabilize the unstable periodic orbit of chaotic spinning disks with incomplete state information. The proposed control structure is based on the T‐S fuzzy systems. This investigation also introduces a new design procedure to satisfy a constraint on the T‐S fuzzy dynamic output feedback control signal. This procedure is independent of the exact value of initial states. Finally, computer simulations are accomplished to illustrate the performance of the proposed control algorithm. © 2015 Wiley Periodicals, Inc. Complexity 21: 148–159, 2016     

Robust H{infty} dynamic output feedback control for 2D linear parameter-varying systems

James Lam Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong Changhong Wang Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, People's Republic of China Corresponding author. Email: ligangwu{at}hit.edu.cn Email: james.lam{at}hku.hk Email: cwang{at}hit.edu.cn Received on June 28, 2006; Accepted on October 1, 2007 This paper is concerned with the problem of robust dynamicoutput feedback control for 2D discrete-time linear parameter-varyingsystems. Given a Fornasini–Marchesini local state-spacesystem with linear varying parameters, our attention is focussedon the design of full-order dynamic output feedback controller,which guarantees the closed-loop system to be asymptoticallystable and has a prescribed disturbance attenuation performance.A sufficient condition for the existence of a desired robustoutput feedback controller is established in terms of parameterizedlinear matrix inequalities, and the corresponding controllersynthesis is cast into a convex optimization problem which canbe efficiently handled by using standard numerical software.A numerical example is provided to illustrate the effectivenessof the proposed design method.     

Finite‐time stability of a class of oscillating systems with two delays

In this paper, we study finite‐time stability of an oscillating system with 2 delays. To derive a bounded of state vector, we use a representation of explicit solution involving 2‐delayed matrix polynomial of 2 indices after deriving some fundamental estimates for such delayed matrix polynomial of 2 indices. A sufficient condition is given. Finally, an example is given to demonstrate the application of the main result.     

Necessary and sufficient conditions for parameter insensitive disturbance-rejection problems with dynamic output feedback

Email: otsuka{at}j.dendai.ac.jp Received on November 11, 2005; Accepted on December 16, 2006 In this paper, necessary and sufficient conditions for the parameterinsensitive disturbance-rejection problem with dynamic outputfeedback which was studied in Otsuka (1999) to be solvable aregiven for the structured uncertain linear systems. Further,necessary and sufficient conditions for the solvability of theproblems with static output feedback and state feedback arealso studied as special cases. The obtained results containsome extensions of the previous results to the structured uncertainlinear systems.     

Finite‐volume scheme for a degenerate cross‐diffusion model motivated from ion transport

An implicit Euler finite‐volume scheme for a degenerate cross‐diffusion system describing the ion transport through biological membranes is proposed. The strongly coupled equations for the ion concentrations include drift terms involving the electric potential, which is coupled to the concentrations through the Poisson equation. The cross‐diffusion system possesses a formal gradient‐flow structure revealing nonstandard degeneracies, which lead to considerable mathematical difficulties. The finite‐volume scheme is based on two‐point flux approximations with “double” upwind mobilities. The existence of solutions to the fully discrete scheme is proved. When the particles are not distinguishable and the dynamics is driven by cross diffusion only, it is shown that the scheme preserves the structure of the equations like nonnegativity, upper bounds, and entropy dissipation. The degeneracy is overcome by proving a new discrete Aubin–Lions lemma of “degenerate” type. Numerical simulations of a calcium‐selective ion channel in two space dimensions show that the scheme is efficient even in the general case of ion transport.     

Analysis of second order and unconditionally stable BDF2‐AB2 method for the Navier‐Stokes equations with nonlinear time relaxation

In this study, we first consider a second order time stepping finite element BDF2‐AB2 method for the Navier‐Stokes equations (NSE). We prove that the method is unconditionally stable and accurate. Second, we consider a nonlinear time relaxation model which consists of adding a term “” to the Navier‐Stokes Equations with the algorithm depends on BDF2‐AB2 method. We prove that this method is unconditionally stable, too. We applied the BDF2‐AB2 method to several numeral experiments including flow around the cylinder. We have also applied BDF2‐AB2 method with nonlinear time relaxation to some problems. It is observed that when the equilibrium errors are high, applying BDF2‐AB2 with nonlinear time relaxation method to the problem yields lower equilibrium errors.     

On the subdomain‐Galerkin/least squares method for 2‐ and 3‐D mixed elliptic problems with reaction terms

In this article we apply the subdomain‐Galerkin/least squares method, which is first proposed by Chang and Gunzburger for first‐order elliptic systems without reaction terms in the plane, to solve second‐order non‐selfadjoint elliptic problems in two‐ and three‐dimensional bounded domains with triangular or tetrahedral regular triangulations. This method can be viewed as a combination of a direct cell vertex finite volume discretization step and an algebraic least‐squares minimization step in which the pressure is approximated by piecewise linear elements and the flux by the lowest order Raviart‐Thomas space. This combined approach has the advantages of both finite volume and least‐squares methods. Among other things, the combined method is not subject to the Ladyzhenskaya‐Babus?ka‐Brezzi condition, and the resulting linear system is symmetric and positive definite. An optimal error estimate in the H¹(Ω) × H(div; Ω) norm is derived. An equivalent residual‐type a posteriori error estimator is also given. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 738–751, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10030.     

3‐D spatio–temporal structures of biofilms in a water channel

We develop a numerical predictive tool for multiphase fluid mixtures consisting of biofilms grown in a viscous fluid matrix by implementing a second‐order finite difference discretization of the multiphase biofilm model developed recently on a general purpose graphic processing unit. With this numerical tool, we study a 3‐D biomass–flow interaction resulting in biomass growth, structure formation, deformation, and detachment phenomena in biofilms grown in a water channel in quiescent state and subject to a shear flow condition, respectively. The numerical investigation is limited in the viscous regime of the biofilm–solvent mixture. In quiescent flows, the model predicts growth patterns consistent with experimental findings for single or multiple adjacent biofilm colonies, the so‐called mushroom shape growth pattern. The simulated biomass growth both in density and thickness matches very well with the experimentally grown biofilm in a water channel. When shear is imposed at a boundary, our numerical studies reproduce wavy patterns, pinching, and streaming phenomena observed in biofilms grown in a water channel. Copyright © 2014 John Wiley & Sons, Ltd.     

Exponential stabilization and L2‐gain for uncertain switched nonlinear systems with interval time‐varying delay

This paper is concerned with the exponential stabilization and L₂‐gain for a class of uncertain switched nonlinear systems with interval time‐varying delay. Based on Lyapunov–Krasovskii functional method, novel delay‐dependent sufficient conditions of exponential stabilization for a class of uncertain switched nonlinear delay systems are developed under an average dwell time scheme. Then, novel criteria to ensure the exponential stabilization with weighted L₂‐gain performance for a class of uncertain switched nonlinear delay systems are established. Furthermore, an effective method is proposed for the designing of a stabilizing feedback controller with L₂‐gain performance. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

A remark on the pressure for the Navier–Stokes flows in 2‐D straight channel with an obstacle

Let T=?×(‐1,1) and &ℴ??² be a smoothly bounded open set, closure of which is contained in T. We consider the stationary Navier–Stokes flows in . In general, the pressure is determined up to a constant. Since Ω has two extremities, we want to know if we can choose the constant same. We study the behaviour of the pressure at the infinity in Ω and give a relation between the velocity and the pressure difference. Copyright © 2004 John Wiley & Sons, Ltd.     

A POD‐based–optimized finite difference CN‐extrapolated implicit scheme for the 2D viscoelastic wave equation†

In this paper, we devote ourselves to establishing the unconditionally stable and absolutely convergent classical finite difference Crank‐Nicholson (CN) implicit (CFDCNI) scheme and optimized finite difference CN‐extrapolated implicit (OFDCNEI) scheme containing very few degrees of freedom but holding fully second‐order accuracy for the two‐dimensional viscoelastic wave via the proper orthogonal decomposition technique, analyzing the existence, stability, and convergence of the CFDCNI and OFDCNEI solutions, and using the numerical simulations to verify that the OFDCNEI scheme is far more superior than the CFDCNI scheme.