Stability Of Time-delay Systems Research Articles

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

In this paper, the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities is investigated. By constructing the new Lyapunov-Krasovskii functional and reduced-order observer, based on homogeneous domination theory together with the adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

New exponentially weighted inequality and its application to finite-time stability of descriptor time-delay systems

The paper considers the finite-time stability of descriptor time-delay systems. Firstly, we establish a set of exponentially weighted orthogonal polynomials, and based on this, we obtain a new exponentially weighted inequality(EWI). Secondly, an augmented Lyapunov-like functional (LLF) is established driven by the presented EWI. Finally, by applying the EWI and the LLF, some sufficient conditions for ensuring the finite-time stability of the system are obtained. A small partial element equivalent circuit model and two numerical examples are used to verify the effectiveness of the method.

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

A novel stability criterion and precise control for linear time delay systems based on regional configuration of the poles

This paper presents the concept of region stability and provides criteria for region stability of linear time delay systems, which can reveal the dynamic and steady-state performance of the systems more precisely. Corresponding design schemes for stabilization and tracking control that can accurately control various performance of time delay systems have also been explored. First, in the light of the connection between the poles and the dynamic properties of the system, the concept of region stability is given to describe the finer dynamic behavior of time delay systems. The criteria for the region stability are also presented. Second, the region stabilization methods are investigated, which can ensure that the system satisfies a certain dynamic performance by setting the eigenvalues in a certain convex region. Third, a precise tracking control of the linear time delay systems is addressed as an application of region stabilization. It can control the steady state performance and transient response of the tracking signal more precisely. Finally, three instances are provided to display the superiority of the new method for the performance indexes of the linear time delay systems.

Safe Stabilization for Stochastic Time-Delay Systems

Safe Stabilization for Stochastic Time-Delay Systems

General single/multiple integral inequalities and their applications to stability of time-delay systems

This paper is concerned with the stability of time delay systems. A new type of multiple integral inner product and a new class of multiple integral inner product space are firstly introduced. Based on them, general single/multiple integral inequalities are developed, and some previous integral inequalities including single and multiple integral inequalities can be regarded as their special cases. Secondly, suitable Lyapunov–Krasovskii functionals (LKF) are constructed. On the basis of the proposed integral inequalities, the derivative of the LKF can be gauged more accurate than those in the literature. As a result, some improved stability criteria of time-delay systems are formulated in terms of linear matrix inequalities. Through two numerical examples, it is shown that these criteria can provide larger delay upper bounds than some existing ones, showing the effectiveness and superiority of the proposed method.

Closing the gap from nominal to robust asymptotic stabilization of time delay systems

SummaryThe control problem of a general class of perturbed linear invariant time‐delay systems within the Sliding Mode Control framework is addressed. We introduce a novel class of sliding manifolds with a structure not previously reported in the literature, which constructively emerges from complete type functionals of the corresponding nominal time‐delay systems and depends on the whole state of the system. A fundamental conclusion derived from this proposal is that every time‐delay system with matched perturbations, whose associated nominal system is exponentially stabilizable, is robustly asymptotically stabilizable. In fact, the introduced sliding manifold enables to construct discontinuous and continuous sliding mode control‐based algorithms that mitigate different classes of perturbations.

Stabilization of time-delay nonlinear systems using Takagi-Sugeno fuzzy models

We propose a controller design method for time-delay nonlinear systems with delays affecting both the states and the inputs, represented by Takagi-Sugeno fuzzy models with nonlinear consequents. To handle the nonlinearities in the consequents we assume that they are slope-bounded. Linear matrix inequality conditions are formulated to design the controller. The obtained results are compared to state-of-the-art approaches and illustrated on two examples.

On the necessity of sufficient LMI conditions for time-delay systems arising from Legendre approximation

This work is dedicated to the stability analysis of time-delay systems with a single constant delay using the Lyapunov–Krasovskii theorem. This approach has been widely used in the literature and numerous sufficient conditions of stability have been proposed and expressed as linear matrix inequalities (LMI). The main criticism of the method that is often pointed out is that these LMI conditions are only sufficient, and there is a lack of information regarding the reduction of the conservatism. Recently, scalable methods have been investigated using Bessel–Legendre inequality or orthogonal polynomial-based inequalities. The interest of these methods relies on their hierarchical structure with a guarantee of reduction of the level of conservatism. However, the convergence is still an open question that will be answered for the first time in this paper. The objective is to prove that the stability of a time-delay system implies the feasibility of these scalable LMI, at a sufficiently large order of the Legendre polynomials. Moreover, the proposed contribution is even able to provide an analytic estimation of this order, giving rise to a necessary and sufficient LMI for the stability of time-delay systems.

Sampled-data output tracking control based on T–S fuzzy model for cancer-tumor-immune systems

This study investigates the tracking control issue for a cancer-tumor immune nonlinear model, which explains the interaction between cancer cells and the immune system in the body. To achieve this, the nonlinear model is first converted into linear sub-models using the Takagi–Sugeno (T–S) fuzzy methodology. The tracking and control of cancer cell proliferation while preserving immune cells is proposed using a sample-data output tracking control technique. Time-dependent discontinuous Lyapunov Krasovskii functional is recommended based on the improved Wirtinger inequality, this may provide additional information about the sawtooth structure of the sampling interval. Less conservative stability criteria are extracted having the form of linear matrix inequalities (LMIs) in consequence of extended reciprocally convex matrix inequality and Wirtinger-based integral inequality. The proposed approach achieves the stabilization of an augmented time delay system that connects with a given fuzzy nonlinear model and tracking error system. Furthermore, the proposed approach reduces the impact of external disturbances under the H∞ norm bound.

Finite-time robust adaptive simultaneous stabilisation of nonlinear time-delay systems with actuator saturation

This paper focuses on finite-time robust adaptive simultaneous stabilisation for nonlinear time-delay systems, taking into account actuator saturation and unknown parameters. Firstly, by employing adaptive control strategies and finite-time stability theory, a finite-time adaptive simultaneous stabilisation scheme for the nonlinear time-delay systems is developed. Secondly, utilising the orthogonal decomposition method, a finite-time robust adaptive simultaneous stabilisation scheme for nonlinear time-delay systems with external disturbances is proposed. Finally, simulations demonstrate the effectiveness of the provided control scheme.

Observer based stabilization of linear time delay systems using new augmented LKF

This paper addresses the stabilization problem of linear time-varying delay systems with unmeasurable states. A novel augmented Lyapunov–Krasovskii functional (LKF) is proposed that effectively accounts for the impact of time delays, and an observer based stabilization controller is developed employing linear matrix inequality (LMI) based optimization technique. The utilization of extended reciprocally convex matrix inequality (ERCMI) is employed in this work to establish less conservative stabilization conditions within the framework of linear matrix inequalities (LMIs). By formulating a convex optimization problem, the observer gain and controller gains are determined. Simulation results are used to validate the design, and two numerical examples are considered to prove the usefulness of the proposed method over existing methods.

Stability of Switching Time Delay Systems

Stability of Switching Time Delay Systems

Improved Stability and Passivity Results for Discrete Time-Delayed Systems with Saturation Nonlinearities and External Disturbances

Improved Stability and Passivity Results for Discrete Time-Delayed Systems with Saturation Nonlinearities and External Disturbances

Growth conditions for global exponential stability and exp-ISS of time-delay systems under point-wise dissipation

Growth conditions for global exponential stability and exp-ISS of time-delay systems under point-wise dissipation

Global rational stabilization of a class of nonlinear time-delay systems

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.

Novel Stability and Stabilization Conditions of Linear Fractional-Order Time-Delay Systems Using Free Matrix Approach

The stability and stabilization problem of linear fractional-order time-delay systems is investigated. By introducing a free matrix, the linear fractional-order time-delay systems is transformed to a delay-free system interconnected with uncertainties. New stability and stabilization criteria are derived based on the small gain theorem. The criteria are formulated as linear matrix inequalities and are computationally efficient. Since the free matrix is utilized, the new conditions are less conservative than the existing ones. Two numerical examples indicate that the proposed criteria are less conservative than existing ones.

Exponential Stabilization for Time-Delay Nonlinear Interconnected Systems With Unknown Control Directions and Unmodeled Dynamics

An exponential stable control scheme based on state transformation and Lyapunov functions is presented for a class of large-scale nonlinear time-delay interconnected systems subjected to unknown control directions and unmodeled dynamics. By regulating the transformed state, the original system state is regulated to the origin at an exponential rate. By introducing a class of type-B Nussbaum functions, the obstacle caused by multiple unknown control coefficients is successfully overcome. Dynamic gains technique and changing supply function idea are established to tackle time-delay terms and unmodeled dynamics in the system. It turns out that the system state converges to the origin at a prescribed speed, and all the closed-loop signals remain bounded. Finally, simulation results show the effectiveness of the proposed methodology.

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.

Robust Stabilization of Linear Time-Delay Systems under Denial-of-Service Attacks.

This research examines new methods for stabilizing linear time-delay systems that are subject to denial-of-service (DoS) attacks. The study takes into account the different effects that a DoS attack can have on the system, specifically delay-independent and -dependent behaviour. The traditional proportional-integral-derivative (PID) acts on the error signal, which is the difference between the reference input and the measured output. The approach in this paper uses what we call the PID state feedback strategy, where the controller acts on the state signal. Our proposed strategy uses the Lyapunov-Krasovskii functional (LKF) to develop new linear matrix inequalities (LMIs). The study considers two scenarios where the time delay is either a continuous bounded function or a differentiable and time-varying function that falls within certain bounds. In both cases, new LMIs are derived to find the PID-like state feedback gains that will ensure robust stabilization. The findings are illustrated with numerical examples.