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EditorialTime-Delay Systems and Their Applications in Engineering 2014

Ligang Wu,1 Hak-Keung Lam,2 Yuxin Zhao,3 and Zhan Shu4

1Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, China2Department of Informatics, King’s College London, London WC2R 2LC, UK3College of Automation, Harbin Engineering University, Harbin 150001, China4Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK

Correspondence should be addressed to Ligang Wu; [email protected]

Received 28 December 2014; Accepted 28 December 2014

Copyright © 2015 Ligang Wu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

It is well known that, together with the increasing expecta-tions of system dynamic performances, the delay informationin practical systems or processes should not be neglectedin the modelling procedure. Time delay is a very commonphenomenon in the engineering world. In fact, many indus-trial processes include after effect phenomena in their innerdynamics. And actuators, sensors, and field networks thatare involved in feedback loops usually introduce unavoidabledelays. The theoretical research about delay related systemsshould be very important, and it is surely a rewardingtopic for researchers. In the past few decades, there hasbeen an increasing interest in time-delayed systems fromcontrol scientists and engineers. On one hand, time delays areinherent in various engineering systems and often deterioratethe main system performances.Those delays can cause insta-bilities of original systems and make it harder for the systemanalysis, controller design or state estimation. To tackle thesedisadvantages, special attention must be paid and necessarycompensation should be applied in the design process. On theother hand, the nice properties of time delays may also bringa new vision for our practical design. For example, if dealtwith properly, the delay elements can really be treated as theoscillation generator or chatting compensator.

In this special issue, most papers are concerned withthe stability analysis and control problems of time-delaysystems. Among them, five papers investigate the simplifiedor improved stability criteria of time-delayed systems; sevenpapers consider the extended stability analysis problems ofthe complex systems with time delay. Based on the existingcontrol theory, three papers discuss the output-feedbackcontrol strategies for the stochastic high-order nonlinear

systems and complex interconnected time-delay systems; onepaper concerns the asymptotic tracking control for a classof nonlinear systems with unknown failures of hystereticactuators; two papers cover the optimal control problem ofthe nonlinear systems with time delay and the calculus vari-ations with time delays; four papers focus on the robustH

∞

or sliding model control schemes of time-delayed dynamicsystems; one paper proposes a novel fractional-order PIDcontroller for integrated pressurized water reactor; and theadaptive and impulsive control concepts are also involved intwo papers. What is more, there are five papers concerningthe observer, filter,monitor, and estimation problems of time-delayed dynamic systems or processes. One paper studies theidentification problem of convex function on Riemannianmanifold.

Stability is the most important problem for time-delaysystems. It is the basic criterion for most of time-delayedcontrol systems. This problem has been intensively studiedduring the past few years. “Modified Schur-Cohn Criterionfor Stability of Delayed Systems” by J. I. Mulero-Martnezgives a modified Schur-Cohn criterion for time-delay lineartime-invariant systems. “New Results on Stability and Sta-bilization of Markovian Jump Systems with Time Delay” byH. Xia et al. deals with the problem of stochastic stabilityand stabilization for a class of linear Markovian jumpinglinear systems with discrete time-varying delay. “ImprovedResults on Robust Stability for Systems with Interval Time-Varying Delays and Nonlinear Perturbations” by X. Zhouet al. investigates delay-dependent robust stability criteriafor systems with interval time-varying delays and nonlinearperturbations. “A Delay Decomposition Approach to the

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 246351, 3 pageshttp://dx.doi.org/10.1155/2015/246351

2 Mathematical Problems in Engineering

Stability Analysis of Singular Systems with Interval Time-Varying Delay” by J. Jiao and R. Zhang investigates delay-dependent stability problem for singular systems with inter-val time-varying delay. “Stability Analysis and H

∞Output

Tracking Control for Linear Systems with Time-VaryingDelays” by K. H. Kim et al. studies the problem of stabilityanalysis and H

∞output tracking control for linear systems

with time-varying delays. “Fixed Points and Stability of aClass of Integrodifferential Equations” by D. Pi studies aclass of integrodifferential functional differential equationswith variable delay. “Robust Stability Analysis of NonlinearFractional-Order Time-Variant Systems” by C. Chen andY. Xie presents a stability theorem for a class of nonlinearfractional-order time-variant systems with fractional-order𝛼 (0 ≤ 𝛼 < 1) by using the Gronwall-Bellman lemma.“Stability and Hopf Bifurcation of a Predator-Prey Modelwith Distributed Delays and Competition Term” by L.-Z.Zheng considers a class of predator-prey systems with dis-tributed delays and competition term. “On Less ConservativeStability Criteria for Neural Networks with Time-VaryingDelays Utilizing Wirtinger-Based Integral Inequality” by O.M. Kwon et al. investigates the problem of stability analysisfor neural networks with time-varying delays. “SimplifiedStability Criteria for Delayed Neutral Systems” by X. Zhanget al. simplifies several existing asymptotic stability criteriain the form of linear matrix inequalities. “Stability Analysisof Fractional-Order Nonlinear Systems with Delay” by Y.Wang and T. Li studies the stability analysis of fractional-order nonlinear systems with delay. “A Less ConservativeStability Criterion for Delayed Stochastic Genetic RegulatoryNetworks” by T. Yu et al. concerns the problem of stabilityanalysis for delayed stochastic genetic regulatory networks.

In order to obtain the desired system performance, somefeasible controllers must be applied to regulate the systemswith time delays. “Robust H

∞Control of Neutral System

with Time-Delay for Dynamic Positioning Ships” by D. Zhaoet al. proposes the less conservative result for the neutralsystem with state-derivative feedback by the delay decom-position approach and linear matrix inequality. “Discrete-Time SlidingMode Control for Uncertain Networked SystemSubject to Time Delay” by S. C. Garcia et al. deals withuncertain systems with networked slidingmode control, sub-ject to time delay. “Adaptive Output Feedback Sliding ModeControl for Complex Interconnected Time-Delay Systems”by H. V. Van et al. extends the decentralized output-feedbacksliding mode control scheme to stabilize a class of complexinterconnected time-delay systems. “Asymptotic TrackingControl for a Class of Nonlinear Systems with UnknownFailures of Hysteretic Actuators” by C. Hou et al. proposesan adaptive failure compensation controller for a class ofnonlinear systems preceded by hysteretic actuators. “A NovelFractional-Order PID Controller for Integrated PressurizedWater Reactor Based on Wavelet Kernel Neural NetworkAlgorithm” by Y. Zhao et al. presents a novel wavelet kernelneural network with wavelet kernel function. “Quasipoly-nomial Approach to Simultaneous Robust Control of Time-Delay Systems” by N. Semenic et al. investigates a controllaw for retarded time-delay systems, concerning infiniteclosed-loop spectrum assignment. “Research on Adaptive

Neural Network Control System Based on Nonlinear U-Model with Time-Varying Delay” by F. Xu et al. proposesa new approach, namely, U-model approach, to solve theproblems of analysis and synthesis for nonlinear systems.“Optimal Control with Time Delays via the Penalty Method”by M. Benharrat and D. F. M. Torres proves necessaryoptimality conditions of Euler-Lagrange type for a problemof the calculus of variations with time delays, where the delayin the unknown function is different from the delay in itsderivative. “RobustMovingHorizonH

∞Control of Discrete

Time-Delayed Systems with Interval Time-Varying Delays”by F. Y. Tascikaraoglu et al. considers the design of a delay-dependent type moving horizon state-feedback control for aclass of linear discrete-time systems subject to time-varyingstate delays, norm bounded uncertainties, and disturbanceswith bounded energies. “Time-Delayed Impulsive Control ofChaotic System Based on T-S Fuzzy Model” by C. Hu and H.Jiang is concerned with the time-delayed impulsive controland synchronization of general chaotic system based on T-Sfuzzy model. “Optimal Control of a Nonlinear Time-DelaySystem in Batch Fermentation Process” by Y. Yu considersan optimal control problem involving a nonlinear time-delaysystem to get a high yield of products in batch process.“Output-Feedback Control for a Class of Stochastic High-Order Feedforward Nonlinear Systems with Delay” by Q.Ma et al. investigates the problem of global output-feedbackstabilization for a class of stochastic high-order time-delayfeedforward nonlinear systems with different power orders.“Adaptive Fuzzy Output-Feedback Method Applied to FinControl for Time-Delay Ship Roll Stabilization” by R. Baiconsiders the ship roll stabilization by fin control system andinvestigates the adaptive fuzzy output-feedback control.

Some specific problems about observer, estimation, mon-itoring, filtering, and identification of time-delay systems andindustrial processes are very important. These topics havebeen analyzed separately. “Observer Design for One-SidedLipschitzNonlinear Systems Subject toMeasurementDelays”by S. Ahmad et al. presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systemsin the presence of output delays. “Estimation of NonlinearFunctions of State Vector for Linear Systems with Time-Delays and Uncertainties” by I. Y. Song et al. focuses onestimation of a nonlinear function of state vector in discrete-time linear systemswith time delays andmodel uncertainties.“H∞

Filtering for Discrete Markov Jump Singular Systemswith Mode-Dependent Time Delay Based on T-S FuzzyModel” by C. Gong and Y. Zeng investigates theH

∞filtering

problem of discrete singular Markov jump systems withmode-dependent time delay based on T-S fuzzy model.“Monitoring of Nonlinear Time-Delay Processes Based onAdaptive Method and Moving Window” by Y. Fan et al.proposes a new adaptive KPCA algorithm for monitoringnonlinear time-delay process. “Experimental Evaluation ofFSM-Based Testing Cost for Time-Delay Systems” by Z. Weiet al. presents a timer embedded FSM model to design acomparative strategy for assessing the coverage criteria andtest suites generation methods for time-delay systems. “H

∞

Filtering forNetworked Systemswith BoundedMeasurementMissing” by H. Yang et al. is concerned with theH

∞filtering

Mathematical Problems in Engineering 3

problem for networked systems with bounded measurementmissing. “The Identification of Convex Function on Rieman-nian Manifold” by L. Zou et al. presents the identification ofconvex function on Riemannian manifold using the Penotgeneralized directional derivative and the Clarke generalizedgradient.

Many practical applications related with time delay arealso concerned with. “Approximate Design of Optimal Dis-turbance Rejection for Discrete-Time Systems with Multi-ple Delayed Inputs: Application to a Jacket-Type OffshoreStructure” by S.-Y. Han et al. is concerned with the problemof optimal disturbance rejection for a class of discrete-time systems with multiple delayed inputs. “The Impactof Awareness Programs with Recruitment and Delay onthe Spread of an Epidemic” by L. Zuo et al. discusses theimpact of awareness programs on the spread and controlof infectious diseases in a given region. “The Applicationof Time-Delay-DependentH

∞Control in the Transmission

Effect of Monetary Policy on Real Estate Market” by H. Guoet al. uses a time-delay-dependent H

∞control method to

analyze the transmission effect of monetary policy on thereal estate market. “Modelling and Simulation of VolumeControlled Mechanical Ventilation System” by Y. Shi et al.derives a new mathematical model of the ventilation system.“Robust PredictiveControl ofWater Level in anExperimentalPilot Plant with Uncertain Input Delay” by F. Q. Rossi and R.K.H.Galvao is concernedwith the predictive control of waterlevel in an experimental pilot plant, in the presence of inputconstraints and uncertain time delays. “Study of RobustH

∞

Filtering Application in Loosely Coupled INS/GPS System”by L. Zhao et al. gives an illustration of minimum meansquare Kalman filter in integration GPS/INS system and acontrast with traditional Kalman filter. “Modeling and Bifur-cation Research of a Worm Propagation Dynamical Systemwith TimeDelay” by Y. Yao et al. adopts both vaccination andquarantine strategy to control the internetwormpropagation.“Global Existence and Uniqueness of Solutions for a FreeBoundary Problem Modeling the Growth of Tumors with aNecrotic Core and a Time Delay in Process of Proliferation”by S. Xu and M. Huang studies a mathematical model for thegrowth of necrotic tumors with time delays in proliferation.

For both the theoretical and practical impact, time-delaysystems have been an enduring theme in the study of differ-ential equations, stochastic processes, statistics theory, andsystems theory.These research topics have broad applicationsto a number of areas such as mechanical, electrical, andchemical engineering. And the theoretical research resultsabout time-delayed systems have played an important rolein solving these delay related problems. Recently, someopen problems about time delay have also emerged, suchas using the delayed inputs to stabilize and regulate theoriginal system, adaptive identification of delays in practi-cal problems, taking advantage of the stochastic propertiesof time delay, and considering the delay information forobservers. Needless to say, these open problems are bothchallenging and rewarding for theoretical researchers andpractical engineers. And many articles in this special issuehave been concerned with these most recent theoreticaldevelopments and practical applications.

Of course, the selected topics and papers are not acomprehensive representation of the area of this specialissue. Nonetheless, they represent the rich and many-facetedknowledge and we hope the readers will find them wellreadable and useful.

Acknowledgments

Wewould like to express our great appreciation to the authorsfor their remarkable contributions in assisting us. Finally, allreviewers’ fundamental work on these papers is also verygreatly acknowledged.

Ligang WuHak-Keung Lam

Yuxin ZhaoZhan Shu

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Editorial Time-Delay Systems and Their Applications in ...downloads.hindawi.com/journals/mpe/2015/246351.pdf · Time-Delay Systems and Their Applications in Engineering 2014 ... Fractional-Order