Continuous Time-delay Systems Research Articles

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers.

In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.

New Insights on Bidirectional Associative Memory Neural Networks with Leakage Delay Components and Time-Varying Delays Using Sampled-Data Control

The sampling data control of bidirectional associative memory (BAM) neural network with leakage delay is considered in this article. The BAM model is viewed as a mixed delay that combines a distributed delay, a discrete delay that varies over time, and a delay in the leaking period. The sampling system is then converted to a continuous time-delay system using an input delay method. In order to get adequate conditions in the form of linear matrix inequalities(LMIs), we build a new Lyapunov-Krasovskii Functional (LKF) in conjunction with the free weight matrix approach. Finally, a simulation results are given to show the efficiency of the theoretical approach.

Attack-tolerant control for Markovian jump systems with stochastic sampling: A sliding mode scheme

This work discusses the sampled-data sliding mode control problem for Markovian jump systems in the presence of Denial-of-Service (DoS) attacks, where the state signals are sampled stochastically and transmitted via vulnerable communication networks. The successful transmitted sequence with double randomness is established, and the probability distribution on both the attacked signals and stochastic delays are given. With the aid of the coordinate transformation, a linear sliding surface is constructed and the mode-dependent sliding mode controller is designed by means of only successfully transmitted state signals. Moreover, the resultant closed-loop systems composed of partial state and sliding mode variable are described as a continuous time-delay system with double randomness depending on the probability distribution characteristics of both the sampling periods and DoS attacks. Both the mean-square exponential ultimate boundedness of the closed-loop system and the reachability of the sliding surface are analyzed and the corresponding sufficient conditions are derived. Meanwhile, an optimization problem with genetic algorithm is formulated for achieving fast convergence of the state trajectory, small ultimate bound of the system state and small sliding bound. Finally, the simulation results via the numerical example are provided to illustrate the proposed sampled-data sliding mode control scheme.

Homogeneous Domination Approach to Global Stabilization of Stochastic Continuous Nonlinear Time-Delay Systems With SISS-Like Conditions

This article aims to investigate the global stabilization for a class of stochastic continuous time-delay nonlinear systems involved with unknown control coefficients and stochastic-input-to-state-stable-like conditions. Without involving the traditional adaptive compensation approach, a dominate gain is adopted to deal with uncertain nonlinearities, which not only include unmeasurable state but also involve input and state delays. On account of homogeneous domination manner and stochastic stability theory, a delay-independent controller is developed to guarantee that the closed-loop system is globally asymptotically stable in probability. Finally, a simulation example is supplied to show the virtue of the devised strategy.

Fully actuated system approaches for continuous-time delay systems: part 2. Systems with input delays

Fully actuated system approaches for continuous-time delay systems: part 2. Systems with input delays

Fully actuated system approaches for continuous-time delay systems: part 1. Systems with state delays only

Fully actuated system approaches for continuous-time delay systems: part 1. Systems with state delays only

Balanced truncation for discrete time-delay systems via the interpretation of system energy

In this paper, the balanced truncation method is investigated for discrete time-delay systems. We show that the energy associated with the system controllability and observability can be characterized via the delay Lyapunov matrices, similar to the case of continuous time-delay systems. Then, we balance the system via a coordinate transformation in order to retain the delay structure of systems naturally. In this way, the balanced truncation method is conducted to obtain structure-preserving reduced models. Further, we provide an efficient process to compute a low-rank approximation to delay Lyapunov matrices based on the equivalent expression of discrete time-delay systems, which enables an approximate but fast execution of the proposed method. The stability of reduced models is also discussed in the paper. Finally, numerical examples are simulated to verify the feasibility and efficiency of the proposed method.

Finite-time and sampled-data synchronization of complex dynamical networks subject to average dwell-time switching signal

This study deals with the finite-time synchronization problem of a class of switched complex dynamical networks (CDNs) with distributed coupling delays via sampled-data control. First, the dynamical model is studied with coupling delays in more detail. The sampling system is then converted to a continuous time-delay system using an input delay technique. We obtain some unique and less conservative criteria on exponential stability using the Lyapunov–Krasovskii functional (LKF), which is generated with a Kronecker product, linear matrix inequalities (LMIs), and integral inequality. Furthermore, some sufficient criteria are derived by an average dwell-time method and determine the finite-time boundedness of CDNs with switching signal. The proposed sufficient conditions can be represented in the form of LMIs. Finally, numerical examples are given to show that the suggested strategy is feasible.

P.094 Evaluate effects of pimavanserin on anxious depression in patients with major depressive disorder - secondary analysis of the CLARITY Study

This paper is devoted to stability analysis of continuous-time delay systems with interval time-varying delays having known bounds on the delay derivatives. A parameterized family of Lyapunov–Krasovskii functionals involving multiple integral terms is introduced, and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time-varying delays. The efficiency of the proposed method is illustrated by numerical examples.

Asymptotic stability analysis and model reduction for spatially interconnected time-delay systems

This paper deals with problems of asymptotic stability analysis and model reduction for spatially interconnected continuous time-delay systems. The well-posedness, asymptotic stability, and contractiveness of spatially interconnected continuous-time state-delay systems are appropriately defined. The Lyapunov–Krasovskii method is extended for asymptotic stability analysis of spatially interconnected continuous time-delay systems in infinite-dimensional space. A sufficient condition based on the given system matrices is presented in terms of linear matrix inequalities to check the well-posedness, asymptotic stability, and contractiveness. We then obtain a sufficient condition for the existence of a delay-free reduced-order system for a given spatially interconnected continuous time-delay system. Employing the elimination lemma and the cone complementary linearization algorithm, we can obtain a delay-free reduced-order system. Finally, two examples are used to demonstrate the effectiveness and applicability of the proposed method.

An exploration of the Razumikhin stability theorem with applications in stabilization of delay systems

In this paper, we establish a new evolution property of Lyapunov functions that satisfy the Razumikhin Stability Theorem conditions. The derived property is shown to be a valid alternative criterion to prove the asymptotic stability of a delay system without calculating the derivative of the Lyapunov function, and it is especially useful in solving stabilization problems for time delay systems when the delay is unknown. As an example application of this derived property, we investigate the stabilization of continuous-time linear systems with an unknown time-varying delay, by proposing a switched low gain feedback control technique that utilizes the derived property. Existing literature on stabilization of continuous time delay systems all require some knowledge, such as an upper bound, of the delay. In this work, by proposing a switched low gain feedback control law utilizing the derived property, we are able to achieve asymptotic stabilization of the system without any knowledge of the delay. Furthermore, the proposed switched low gain feedback law also significantly improves the closed-loop system performance in terms of overshoot and convergence speed, in comparison with the traditional fixed gain low gain feedback design. Simulation study verifies the theoretical results.

A study on the fatigue of bus drivers based on biological models

In order to improve the fatigue detection ability of public transport drivers, the biometric modelling method is used to test and evaluate the fatigue of drivers. A fatigue detection model for public transport drivers is proposed based on biological mathematical model analysis and the prevention and evaluation according to the fatigue test model is constructed. According to the visual, neural and blood supply characteristics of public transport drivers, the mathematical model of quantitative recursive statistical analysis of public transport drivers' biological fatigue is established by using descriptive statistical analysis method. The problem of public transport driver testing is transformed into an optimal solution problem for a continuous time-delay non-smooth system. Under the condition of non-smooth autonomous continuous boundedness, a biologic mathematical model of fatigue detection is constructed. The delay-dependent sufficient conditions of public transport driver fatigue testing are obtained to prevent and monitor driving fatigue accurately. The test results show that the model is accurate for public traffic drivers' fatigue testing. According to the biometric test results, it can reliably reflect whether the driver is tired or not, so that the danger alarm can be carried out and the driving safety can be ensured.

A study on the fatigue of bus drivers based on biological models

In order to improve the fatigue detection ability of public transport drivers, the biometric modelling method is used to test and evaluate the fatigue of drivers. A fatigue detection model for public transport drivers is proposed based on biological mathematical model analysis and the prevention and evaluation according to the fatigue test model is constructed. According to the visual, neural and blood supply characteristics of public transport drivers, the mathematical model of quantitative recursive statistical analysis of public transport drivers' biological fatigue is established by using descriptive statistical analysis method. The problem of public transport driver testing is transformed into an optimal solution problem for a continuous time-delay non-smooth system. Under the condition of non-smooth autonomous continuous boundedness, a biologic mathematical model of fatigue detection is constructed. The delay-dependent sufficient conditions of public transport driver fatigue testing are obtained to prevent and monitor driving fatigue accurately. The test results show that the model is accurate for public traffic drivers' fatigue testing. According to the biometric test results, it can reliably reflect whether the driver is tired or not, so that the danger alarm can be carried out and the driving safety can be ensured.

Exponential stability of homogeneous impulsive positive delay systems of degree one

This paper investigates the global exponential stability of homogeneous impulsive positive delay systems of degree one. By using the max-separable Lyapunov functions, a sufficient criterion is obtained for exponential stability of continuous-time homogeneous impulsive positive delay systems of degree one. We also provide the corresponding counterpart for discrete-time homogeneous impulsive positive delay systems of degree one. Our results show that a stable impulse-free system can keep its original stability property under certain destabilising impulsive perturbations. It should be noted that it's the first time that the exponential stability results for homogeneous impulsive positive delay systems of degree one are given. Numerical examples are provided to demonstrate the effectiveness of the derived results.

Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control

This paper investigates state estimation for complex dynamical networks (CDNs) with time-varying delays by using sampled-data control. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling state estimator is transformed into a continuous time-delay system with stochastic parameters in the system matrices, where the purpose is to design a state estimator to estimate the network states through available output measurements. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) containing triple and fourth integral terms and applying Wirtinger-based single and double integral inequality, Jenson integral inequality technique, delay-dependent stability conditions are established. The obtained conditions can be readily solved by using the LMI tool box in MATLAB. Finally, a numerical example is provided to demonstrate the validity of the proposed scheme.

Finite-time synchronization of sampled-data T–S fuzzy complex dynamical networks subject to average dwell-time approach

The problem of finite-time synchronization for Takagi–Sugeno (T–S) fuzzy complex dynamical networks with coupling delays via sampled-data control is presented in this paper. To change the sampled-data control system into a continuous time-delayed system, an input delay approach is applied. Based on the Lyapunov stability theory, a suitable Lyapunov–Krasovskii functional (LKF) is constructed with the Kronecker products. Furthermore, by applying the average dwell-time approach, a novel sufficient condition is established to ascertain the finite-time stabilization of fuzzy complex dynamical networks (CDNs) with switching signals. The proposed method is less conservative than conventional approaches, since the newly developed time-dependent fuzzy LKF is used. The proposed sufficient condition can be represented in the form of linear matrix inequalities (LMIs). Finally, the effectiveness and superiority of the proposed approach is validated through both numerical and practical examples.

Quantized feedback stabilization of continuous time-delay systems subject to actuator saturation

In this paper, the problem of quantized feedback stabilization is investigated for continuous time-delay systems subject to actuator saturation. By utilizing two different methods, delay-independent conditions are obtained to guarantee the existence of a region of admissible initial conditions from which all trajectories of the resulting closed-loop system converge to a neighborhood of the equilibrium. Furthermore, delay-dependent conditions are developed based on the delay partitioning idea and the Lyapunov–Razumikhin functional approach, respectively. Finally, several examples are provided to demonstrate the effectiveness of the proposed approaches.

Exponential Stability Analysis and Stabilization for Continuous Time-Delay Systems With Controller Failure

In this brief, we study the problem of controller synthesis for time-delay systems with controller failures based on an input–output approach. First, the time-delay system with controller failure is modeled as an input–output form. Next, the stability condition of the system with controller failure is developed via scaled small gain theorem. Additionally, the proposed stability condition is also testified by the direct Lyapunov functional method. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new model of the investigated system, a new triangle inequality and a new Lyapunov–Krasovskii functional. The proposed stability condition is demonstrated to be less conservative than other existing results. Moreover, the problem of stabilization is further solved with admissible controller designed via convex optimizations. The effectiveness of the proposed method is also illustrated via a numerical example.

Online Algebraic Identification Approach of Continuous Linear Time Delay Systems

AbstractIn this paper, we propose an online algebraic method to identify linear continuous time delay process from step response, in presence of unknown initial state and constant load disturbance. The identification mechanism is split into two sequential steps. The time delay and dynamic of the plant is estimated firstly through a spectral formulation. In the next stage, the transient regime is deduced from a linear regression. To improve the robustness of the proposed method, a local convolution by sigmoid function is proposed. Simulation results are provided, at last, to show the effectiveness of our conceived approach.

Stability analysis of linear systems with interval time-varying delays utilizing multiple integral inequalities

This paper is devoted to stability analysis of continuous-time delay systems with interval time-varying delays having known bounds on the delay derivatives. A parameterized family of Lyapunov–Krasovskii functionals involving multiple integral terms is introduced, and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time-varying delays. The efficiency of the proposed method is illustrated by numerical examples.