Class Of Time-delay Systems Research Articles

Refined Jensen‐based inequality approach to stability analysis of time‐delay systems

In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time-delay systems. More precisely, by using the newly derived inequalities, they establish new stability criteria for two classes of time-delay systems, namely discrete and distributed constant delays systems and interval time-varying delay systems. The resulting stability conditions are derived in terms of linear matrix inequalities, which can be efficiently solved by various convex optimisation algorithms. Numerical examples are given to show the effectiveness and least conservativeness of the results obtained in this study.

Adaptive-gain observer-based control of a class of time-delay systems subject to output-slope non-linearities

A non-linear adaptive observer is proposed to estimate the unmeasured states of a class of time-delay non-linear systems. Irrespective of the size of the constant delay, it is shown that the observer is globally convergent if the growth rate of the system non-linearities is output dependent. The presented results generalize previous results on observation of Lipschitz time-delay systems. Subsequently, the observerbased control problem of time-delay systems, having triangular structure, is discussed for arbitrary large constant delay.

Study and Application of State Estimator for Time-Delay Systems with State Saturation Nonlinearities

The design and application of state estimator for a class of time-delay systems with state saturation nonlinearities are firstly explored. Based on the Lyapunov-Razumikhin functions, delay-dependent sufficient conditions are established to guarantee the asymptotic stability of the error between the state estimate and the true state. Besides, an upper bound of arbitrary time-varying delays is derived to assure that the resulting error can converge asymptotically to zero. Finally, applications to the secure communication and simulation results are given to demonstrate the feasibility and effectiveness of the main results.

New Result on Low-Order Controller Design for First-Order Delay Processes via Eigenvalue Assignment

This article developed a new result on the eigenvalue distribution for a certain class of time delay systems based on the extension of the Hermite-Biehler Theorem. Such result is applied to proportional-integral (PI) controller parameter design for a first-order plant with time delay via eigenvalue assignment. Using the method provided in this paper, one can assign the rightmost eigenvalues of the closed-loop system to desired positions in the complex plane. Further, on the basis of the previous result, this paper also extended the PI control to the proportional-integral-derivative (PID) case.

State Estimation for Time-Delay Systems with Markov Jump Parameters and Missing Measurements

This paper is concerned with the state estimation problem for a class of time-delay systems with Markovian jump parameters and missing measurements, considering the fact that data missing may occur in the process of transmission and its failure rates are governed by random variables satisfying certain probabilistic distribution. By employing a new Lyapunov function and using the convexity property of the matrix inequality, a sufficient condition for the existence of the desired state estimator for Markovian jump systems with missing measurements can be achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Furthermore, the gain of state estimator can also be derived based on the known conditions. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed method.

基于输出时滞方法的采样数据系统故障估计

The problem of fault estimation for a class of non-uniformly sampled-data systems is investigated from the time delay point of view in this paper. Firstly, the output delay approach is employed to model the sampled-data system as a continuous-time one with time-varying delay output. Then, based on the analysis of the inapplicability of the adaptive fault diagnosis observer in such class of time-delay systems, a novel augmented fault estimation observer design method is proposed to guarantee the exponential convergence of the estimation errors. Furthermore, an extension to the case of time varying fault estimation for the noisy sampled-data systems is studied. Finally, simulation results of a flight control system are presented to demonstrate the effectiveness of the proposed method.

Exact stability analysis of second-order leaderless and leader–follower consensus protocols with rationally-independent multiple time delays

An investigation of double-integrator agents with directed asymmetric consensus protocols and multiple rationally independent time delays is presented in this paper from two novel perspectives. First, we complement the group consensus literature on crucial stability analysis, using a recent technique called the Cluster Treatment of Characteristic Roots (CTCR) for the first time on this class of time-delayed systems. The CTCR paradigm is pursued after a block-diagonalization (mode-decoupling) transformation on the system. This treatment produces some unique stability tables for the dynamics in the space of the delays which are non-conservative and exhaustive. Second, a novel concept of spectral delay space is presented, as an overture to the CTCR for the determination of the complete set of stability-crossing (switching) hypersurfaces in the delay space. Examples are provided to display the strengths and efficiency of this new stability analysis mechanism.

Robust and NonfragileH∞Kalman-Type Filter Design for Parameter-Uncertain Time-Delay Systems: PLMI Approach

This paper describes the synthesis of a robust and nonfragileH∞Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragileH∞filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragileH∞filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

Robust Fault Tolerant Control for a Class of Time-Delay Systems with Multiple Disturbances

A robust fault tolerant control (FTC) approach is addressed for a class of nonlinear systems with time delay, actuator faults, and multiple disturbances. The first part of the multiple disturbances is supposed to be an uncertain modeled disturbance and the second one represents a norm-bounded variable. First, a composite observer is designed to estimate the uncertain modeled disturbance and actuator fault simultaneously. Then, an FTC strategy consisting of disturbance observer based control (DOBC), fault accommodation, and a mixedH2/H∞controller is constructed to reconfigure the considered systems with disturbance rejection and attenuation performance. Finally, simulations for a flight control system are given to show the efficiency of the proposed approach.

Memory State-Feedback Stabilization for a Class of Time-Delay Systems with a Type of Adaptive Strategy

Stabilization of a class of systems with time delay is studied using adaptive control. With the help of the “error to error” technique and the separated “descriptor form” technique, the memory state-feedback controller is designed. The adaptive controller designed can guarantee asymptotical stability of the closed-loop system via a suitable Lyapunov-Krasovskii functional. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality (LMI) design approach. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.

Robust <i>H<sub>∞</sub></i> Control of Time-Delay Systems

In this paper, a delay-dependent H_infinity performance criterion which possess decoupling structure is derived for a class of time-delay systems. It is then extended to H_infinity state-feedback synthesis for time-delay systems with polytopic uncertainty. All the conditions are given in terms of the linear matrix inequalities (LMIs). Numerical examples illustrate the effectiveness of our methods.

New Results to Verify the Robust Stability Property of Interval Plants with Time-Delay

This paper presents a sufficient condition to verify the robust stability property of a class of time delay systems which are described as an interval plant with uncertain time delay. The main result is obtained on the basis of some polynomials that can be easily computed using Kharitonov's polynomials. This contribution considers the delay with interval uncertainty, since in most of the research reports only fixed delay is considered. The present work bases its results on the value set characterization for interval plants with uncertain time delay along with the use of the zero exclusion principle to compute the robust stability property of the close loop system.

An output delay approach to fault estimation for sampled-data systems

The problem of fault estimation for a class of non-uniformly sampled-data systems is investigated from the time delay point of view in this paper. Firstly, the output delay approach is employed to model the sampled-data system as a continuous-time one with time-varying delay output. Then, based on the analysis of the inapplicability of the adaptive fault diagnosis observer in such class of time-delay systems, a novel augmented fault estimation observer design method is proposed to guarantee the exponential convergence of the estimation errors. Furthermore, an extension to the case of time varying fault estimation for the noisy sampled-data systems is studied. Finally, simulation results of a flight control system are presented to demonstrate the effectiveness of the proposed method.

A VERY SIMPLE CRITERION FOR CHARACTERIZING THE CROSSING DIRECTION OF TIME-DELAY SYSTEMS WITH DELAY-DEPENDENT PARAMETERS

In this paper, a very simple criterion has been established for checking the crossing direction of a characteristic root crossing the imaginary axis for a class of time-delay systems with delay-dependent parameters, an important topic both in stability analysis and Hopf bifurcation. The criterion uses two easy-to-obtain functions with clear physical meaning from the critical stability condition and it generalizes a popular result in the literature.

Control of dead-time systems using derivative free particle swarm optimisation

Particle swarm optimisation (PSO), a population-based nature inspired algorithm has mostly been used for solving continuous optimisation problems, discrete variants also exist. It finds application in most of the engineering design problems. This paper introduces two improved forms of PSO algorithm applied to PID controller and Smith predictor design for a class of time delay systems. In this paper, derivative free optimisation methods, namely simplex derivative pattern search and implicit filtering are used to hybridise PSO algorithm with improved convergence than original PSO. The effectiveness of the proposed algorithms namely SDPS-PSO, IMF-PSO are demonstrated using unit step set point response for a class of dead-time systems using PID controller and Smith predictor designed using the proposed hybrid PSO algorithms. The results are compared with earlier controller tunings proposed by Kookos, Syrcos, Chidambaram, Kanthaswamy and Luyben.

Robust stabilizing first-order controllers for a class of time delay systems

In this paper, stabilizing regions of a first-order controller for an all poles system with time delay are computed via parametric methods. First, the admissible ranges of one of the controller’s parameters are obtained. Then, for a fixed value of this parameter, stabilizing regions in the remaining two parameters are determined using the D-decomposition method. Phase and gain margin specifications are then included in the design. Finally, robust stabilizing first-order controllers are determined for uncertain plants with an interval type uncertainty in the coefficients. Examples are given to illustrate the effectiveness of the proposed method.

Robust stabilization of a class of uncertain systems with time delay

In this paper, the problem of stabilizing uncertain systems with time delay by low order controllers is considered. The set of all stabilizing controllers, having three parameters, are determined for this class of time delay systems. First, the D-decomposition method is employed to solve the problem for plants without uncertainty. The approach consists of using two subsidiary quasi-polynomials. Next, the convex direction concept together with Kharitonov plants are used to solve the original problem. Examples are given to illustrate the application of the proposed method.

Stability Study of an Observer-Based Controlled Wind Turbine

In this paper, the problem of stabilizing uncertain systems with time delay by low order controllers is considered. The set of all stabilizing controllers, having three parameters, are determined for this class of time delay systems. First, the D-decomposition method is employed to solve the problem for plants without uncertainty. The approach consists of using two subsidiary quasi-polynomials. Next, the convex direction concept together with Kharitonov plants are used to solve the original problem. Examples are given to illustrate the application of the proposed method.The aim of this paper is to analyze the quadratic stability of a gain scheduled observer-based state feedback controlled wind turbine. The designed control law consists in a linear quadratic regulator combined to a multimodel approach to deal with the high nonlinearity of the studied plant. Since the state variables of the considered process are not all measureable, a state observer is necessary to estimate the immeasurable ones. Hence the asymptotic stability study of the augmented system is considered by using the Lyapunov direct method associated to the resolution of an LMI feasibility problem.

L2-gain Analysis and Feedback Design for a Class of Time-delay Systems with Discontinuity

This paper investigates the L2-gain analysis and synthesis issues under the Filippov framework for a class of nonlinear time-delay systems with discontinuity. First, an extension of L2-gain property along all the Filippov solutions is given for the time-delay systems, and a sufficient condition is presented that guarantees the nonlinear time-delay systems is strongly stable in the sense of Filippov solution, and the L2-gain less than a given level. The condition is described by functional partial differential inequality. Then, as an application of the presented condition, a feedback control design problem is solved that the controller strongly stabilized a given plant with pre-specified L2-gain. Furthermore, as a special case study, the case of linear systems is discussed and it is shown that for the piecewise continuous linear systems, the sufficient condition is represented by algebraic Riccati inequalities.

A Combined Simple Adaptive Control with Disturbance Observer for a Class of Time-Delay Systems

Disturbance attenuation for a class of time-delay systems is performed by a combined simple adaptive control (SAC) with a new configuration of disturbance observer (DOB). The nominal system results from the Pade approximation, which is in the form of a non-minimum phase LTI system. For the implementation of SAC and DOB, two parallel feedforward compensators (PFC) are designed with the inverses of PD- and PID-controller, respectively. Simulation results show the effectiveness of the proposed controller to compensate the disturbance response and uncertain delay time.