Time-varying State Delays Research Articles

Dynamic IQC-Based Control of Uncertain LFT Systems With Time-Varying State Delay.

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the L2 -gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired L2 -gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies.

Passivity-based stabilization and passive synchronization of complex nonlinear networks

This paper investigates the passive stabilization and passive synchronization problems for complex nonlinear networks. Two classes of complex networks are considered with or without time delays (including the state time-varying delays, feedback time-varying delays and interconnection time-varying delays). The purpose of passive stabilization and passive synchronization is to design a state feedback controller such that the nonlinear dynamical network and the corresponding error dynamical network are passive and stable asymptotically. Delay-independent sufficient conditions for complex nonlinear networks without delays and delay-dependent sufficient conditions for complex nonlinear networks with time-varying delays are provided, respectively, to solve the passive stabilization and passive synchronization problems for the given networks. Two numerical examples are employed to illustrate the effectiveness of the proposed results.

An LMI-based controller design method for a discrete-time linear system with time-varying state delays

An LMI-based controller design method for a discrete-time linear system with time-varying state delays

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.

Output feedback regulation of a chain of integrators with unknown time-varying delays in states and input

We consider a problem of global asymptotic regulation of a chain of integrators that has unknown time-varying delays in both states and input by output feedback. The time-varying delays are only known to be bounded, and their bounds and time-varying rates are unknown. To solve the considered problem, we introduce a newly designed adaptive output feedback controller. For system analysis, we give a new transformation and techniques in order to deal with new phenomena associated with unknown time-varying delays in states.

Robust H<sub>∞</sub> Control for Takagi-Sugeno Fuzzy Systems with Time-Varying Delays in State and Input

In this paper, the robust H∞ stabilization problem for Takagi-Sugeno fuzzy control systemswith state and input delays is explored. Based on a Lyapunov-Krasoviskii function, the delaydependentstabilization conditions are proposed in terms of linear matrix inequalities (LMIs) to guaranteethe asymptotic stabilization of time-delay Takagi-Sugeno fuzzy systems with disturbance input.Finally, a numerical example is illustrated to demonstrate the feasibility and effectiveness of the proposed stabilization.

State estimation for uncertain discrete-time stochastic neural networks with Markovian jump parameters and time-varying delays

The state estimation problem is considered for a class of discrete-time stochastic neural networks with Markovian jumping parameters in this paper. Norm-bounded parameter uncertainties in the state and measurement equation and time-varying delays are investigated. The neuron activation function satisfies sector-bounded conditions, and the nonlinear perturbation of the measurement equation satisfies standard Lipschitz condition and sector-bounded conditions. By constructing proper Lyapunov–Krasovskii functional, delay-dependent conditions are developed in terms of linear matrix inequalities (LMIs) to estimate the neuron state such that the dynamic of the estimation error system is asymptotically stable. Finally, numerical examples are shown to demonstrate the effectiveness and applicability of the proposed design method.

Advances in Control Theory and Applications: Selected papers from TOK 2013

The Turkish National Committee of Automatic Control (TOK) is the National Member Organization (NMO) of IFAC in Turkey. The TOK meeting is a major national meeting on automatic control, which has been organized annually since 1994 with the aim of reporting on recent advances in control theory and applications in Turkey. The 15th TOK national meeting (TOK 2013) was held at Inonu University in Malatya, Turkey, on 26–28 September 2013. It was organized by Inonu University and Istanbul Technical University, and supported by TOK. All papers submitted to TOK 2013 were reviewed by three separate reviewers; 185 papers were accepted for oral presentation and 63 papers for poster presentation. The TOK 2013 technical programme consisted of 31 oral sessions (three being special sessions) and four poster sessions. The programme also included three plenary lectures, given by leading experts in the field – Professors Derek P. Atherton from the University of Sussex, UK, YangQuan Chen from the University of California, Merced, USA, and _ Ismail Yuksek from Yildiz Technical University, Turkey. A preconference workshop programme was organized on 25 September, with lectures presented by Professor Derek P. Atherton and Professor YangQuan Chen. All accepted papers for TOK 2013, which were written in Turkish, were screened for this special issue of the Transactions of the Institute of Measurement and Control. Eleven papers were selected and extended versions, written in English, were further reviewed by three different reviewers, whom we thank for their efforts. These papers constitute this special issue. ‘Design of a multiple-model switching controller for ABS braking dynamics’, by M. Dousti, S.C. Baslamisli, E. T. Onder and S. Solmaz: the purpose of this study is to design high-performance active braking control and observer algorithms for passenger vehicles equipped with electromechanical brake systems. These algorithms are designed to be adaptive with changing driving and road conditions in a switched multiple-model manner to ensure high performance and robustness. The effectiveness of a set of multiple-model switching lead-lag controllers is evaluated during transitions between different road friction coefficients. Meanwhile, a multiple-model switching observer algorithm is developed to estimate the shape of the tyre braking force curve with respect to the longitudinal slip. Each switched observer predicts signals according to its preset tyre model. The observers are designed based on different Burckhardt tyre models that are parameterized for different road conditions. In the simulations, the value of the friction coefficient is assumed to be unknown and our switching algorithms are observed to estimate successfully the varying friction coefficients by comparing a quadratic cost function of measured signals from the vehicle with signals generated by observers. It is demonstrated that the proposed algorithms provide high reliability and fast response, thus ensuring a stopping distance close to the theoretical minimum. ‘Receding horizon HN control of time-delay systems’, by F.Y. Tas xc xikaraoglu, L. Ucun and I.B. Kuc xukdemiral: this paper deals with the disturbance rejection problem for discrete-time linear systems having time-varying state delays and control constraints. The study proposes a novel receding horizon HN control method utilizing a linear matrix inequality based optimization algorithm, which is solved in each step of run-time. The proposed controller attenuates disturbances having bounded energies on controlled output, and ensures the closed-loop stability and dissipation while meeting the physical control input constraints. The originality of the work lies on the extension of the idea of the well-known HN receding horizon control technique developed for linear discretetime systems to interval time-delay systems having timevarying delays. The efficiency of the proposed method is illustrated through simulation studies that are carried out on a couple of benchmark problems. ‘Stability region analysis in Smith predictor configurations using a PI controller’, by F.N. Deniz, N. Tan, S.E. Hamamci and I. Kaya. This paper deals with the stabilization problem

Adaptive compensation for actuator failure in a class of non‐linear time‐delay systems

This study presents a state feedback adaptive controller for a class of parametric-strict-feedback non-linear systems with multiple bounded time-varying state delays and in the presence of time-varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some unknown time-varying values where the parameters, times and patterns of the failures are also unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. The adaptive state feedback control scheme is constructed based on a backstepping design method. The boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighbourhood of the origin. The proposed approach is employed for a second-order time delay plant as well as a two-stage chemical reactor with delayed recycle streams. The simulation results show the correctness and effectiveness of the proposed adaptive compensation in the case of actuator failures.

Decentralized piecewise [formula omitted] fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay

This paper investigates the problem of decentralized piecewise H∞ filtering design for a class of discrete-time large-scale nonlinear systems with time-varying delay. The considered large-scale system consists of a number of nonlinear subsystems, and each nonlinear subsystem is represented by a Takagi–Sugeno (T–S) model. The time-varying state delay of each subsystem is assumed to be of an interval-like type with lower and upper bounds. The objective is to design a decentralized piecewise filter such that the filtering error system is asymptotically stable with a guaranteed H∞ disturbance attenuation level. A two-term approximation method is proposed to transform the filtering error system into an interconnected formulation, and the decentralized H∞ filtering problem is reformulated in the context of input–output (IO) stability. Based on a piecewise Lyapunov–Krasovskii functional (PLKF) combined with the scaled small gain (SSG) theorem, less conservative results are presented for the decentralized piecewise H∞ filtering design of the large-scale T–S fuzzy system in terms of linear matrix inequalities. Two examples are provided to illustrate the effectiveness of the proposed method.

Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying.

Stabilization of Uncertain Systems with Both State and Control Delays

This paper is devoted to the stability and stabilization problem for uncertain and nonlinear systems with time-varying state delay and network induced control delay. The class of admissible uncertainties and nonlinearities of the system comprehends several types of uncertainties frequently investigated in the literature. Using some recent developments, new sufficient conditions are established for the analysis and the control design expressed by linear and bilinear matrix inequalities, respectively. These conditions are obtained via the Lyapunov-Krasovskii method. Numerical examples illustrate the effectiveness of the proposed method.

Delay-Interval-Dependent Stability Criterion for Linear Systems With Time-Varying State Delay

This paper considers the problem of stability analysis of linear systems with a time-varying state delay. A new delay-interval-dependent stability criterion is derived without involving any direct approximation of the integral terms that involve uncertain limit of integration in the time-derivative of the Lyapunov-Krasovskii functional. This development leads to a less conservative LMI criterion as seen through numerical examples.

Integrated Fault Detection for Two-Dimensional Discrete Systems with Time-Varying Delays

Integrated fault detection (FD) for two-dimensional (2-D) discrete systems with time-varying state delays is studied in this paper. The concerned 2-D time-varying delay systems are described by the Fornasini-Marchesini second model and are subject to unknown disturbances. An integrated residual generation and evaluation design based on descriptor-system-approach observer is proposed for acquiring the occurrences of sensor fault. Such an integrated design can maximize the fault detection rate for a given false alarm rate. Sufficient conditions for the existence of the integrated FD design are derived in the context of time domain norm evaluation and provided in terms of matrix inequalities. A thermal process plant is provided to illustrate the effectiveness of the proposed method.

New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.

Exact tracking control of nonlinear systems with time delays and dead-zone input

This paper is concerned with the control design problem for a class of nonlinear systems with the state time-varying time delays and nonsymmetric dead zone. The problem addressed is to design adaptive controllers that guarantee the exact tracking of a given reference signal. Two continuous robust adaptive control schemes are proposed. A positive nonlinear control gain function, which is not required to satisfy an inequality but is expressed explicitly, is carefully constructed and is used in the control law and adaptive law. An illustrative example is provided to demonstrate the validity of the proposed design method.

MRAC of systems subject to actuator nonlinearities and unknown time-varying state delays: tube reference approach

In this contribution, a tube based model reference adaptive architecture is developed for a class of nonlinear dynamic systems with unknown time-varying state delay and nonlinear actuator which not only guarantees closed loop stability, asymptotically tracking and robustness to a nonlinear perturbation, and to an external disturbance with unknown bounds, but also diminishes the control cost with respect to some criterion.

Stability and Stabilization of Takagi-Sugeno Fuzzy Systems via Sampled-Data and State Quantized Controller

In this paper, we investigate the problem of stability and stabilization for sampled-data fuzzy systems with state quantization. By using an input delay approach, the sampled-data fuzzy systems with state quantization are transformed into a continuous-time system with a delay in the state. The transformed system contains nondifferentiable time-varying state delay. Based on some integral techniques, some new stability and stabilization criteria are first proposed by a modified Lyapunov functional. Furthermore, in the case of no quantization, some new stability and stabilization criteria are also obtained. It is shown that the new stability and stabilization criteria can provide a larger upper bound of the sampling interval than some existing ones in the literature. Two simulation examples are given to show the effectiveness of the proposed design method.

Comments on ‘Improved delay-dependent stability criteria for continuous systems with two additive time-varying delay components’

In this write-up, comments on the omission of few important inequality conditions (or constraints) in the LMI optimization problem stated as delay-dependent stability criterion for a class of linear systems with two additive time-varying state-delays in Cheng et al. (2014) is reported. The omission paves way to incorrectness of the published result. The consequence of the omission, and the revised result are presented in the sequel.

Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach

This paper is concerned with the problem of robust fault estimation and fault-tolerant control for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying state delay and actuator faults. Based on the ( $k-1$ )th fault estimation information, a novel $k$ -step fault-estimation observer is proposed to construct the $k$ th fault error dynamics. The obtained fault estimates via $k$ -step fault-estimation can practically better depict the size and shape of the faults. Then, based on the information of online $k$ -step fault-estimation, a dynamic output feedback fault tolerant controller is designed to compensate the fault effects on the closed-loop fuzzy system. Furthermore, some less conservative delay dependent sufficient conditions for the existence of fault estimation observers and fault tolerant controllers are given in terms of solution to a set of linear matrix inequalities. Finally, simulation results of two numerical examples are presented to show the effectiveness and merits of the proposed methods.