Singular Time-delay Systems Research Articles

Disturbance rejection analysis of singular time-delay systems based on state decomposition method

The state decomposition technique (SDT) based on memory state-feedback control (MSFC) is used in this article to provide a new disturbance-rejection (DR) method for singular time-delay systems (STSs). First, under MSFC, a singular time-delay control system with disturbance estimator is constructed. Then, a DR control law, which contains disturbance information and MSFC, is designed. Second, the STS is split into algebraic and differential subsystems based on the SDT. Next, a brand-new enhanced Lyapunov–Krasovskii function (LKF) with fewer state vectors is designed. Additionally, a new delay-dependent admissible criterion with fewer decision variables is obtained based on the LKF by combining a Jensen inequality and two zero equations. Third, the controller is designed according to the decomposition component of the controller gain. Finally, the usefulness and efficiency of the strategy are demonstrated by comparing it to a sliding mode control and a traditional control technique.

A further step to transient performance enhancement of discrete-time singular systems with time-varying delay

This paper is the first attempt to enhance the transient performance while simultaneously addressing the output regulation challenges for discrete singular time-delay systems subject to actuator saturation. The proposed controller consists of two linear and nonlinear parts, without any switching elements. The linear part is designed to solve the main regulation problem, while the nonlinear part is designed to enhance the performance of the closed-loop system in the face of input saturation. The delay-range dependent stability conditions of the closed-loop system are analysed using the Lyapunov-Krasovskii (LK) approach, which involves solving an LMI problem to determine the parameters of the proposed controller. Furthermore, the admissibility of the closed-loop system is assessed to ensure the system’s stability, regularity, and causality. Finally, the theoretical achievements are endorsed by simulations through numerical and practical examples.

Exponential stabilization of hybrid event‐triggered singular time‐delay systems

The exponential stability of hybrid event‐triggered singular time‐delay (STD) systems is established in this paper. To ensure their exponential stability, we give sufficient conditions for linear matrix inequalities (LMIs) for STD systems with average impulsive gain. Furthermore, zeno behavior is avoided by carefully designing the settings for event‐triggering conditions. A few numerical examples demonstrate the usefulness of the suggested findings.

A new [formula omitted] control method of singular time-delay systems based on a variable memory state feedback

This paper is concerned with the H∞ control problem of singular time-delay systems. A variable memory state feedback is established with state decomposition. It is verified that this feedback including the traditional memory and memoryless state feedbacks as special cases, and thus it is more general than these existing feedback strategies Based on the proposed feedback, a new H∞ control method with better performance level is derived. Moreover, the yielded computational complexity is lower. The superiority is confirmed by two given examples.

Toward transient performance enhancement of constrained switched singular time-delay systems

Transient performance is a highly valued factor in real control systems. Having a suitable transient performance not only guarantees the safety of the system but also makes the response more desirable by reducing transient factors like the overshoot and the settling time. This paper is the first attempt to design a novel controller to improve the transient performance of switched singular time-delay systems. The proposed controller comprises a combination of linear and nonlinear parts. First, a linear part is designed to fulfill the stabilisation. Then a nonlinear part is added to it to improve the transient response. The admissibility of the closed-loop system is investigated through some given theorems based on the Lyapunov-Krasovskii approach. The closed-loop system’s regularity and impulse freeness are also guaranteed in the given theorems. Computer simulation of some numerical and practical examples will endorse the theoretical achievements afterward.

P-Accelerated normal S-iterative learning control algorithm for linear discrete singular time-delay systems

This article addresses the issue of iterative learning control for a specific category of discrete linear singular time-delay systems. A new iterative learning control algorithm based on the p-accelerated normal S-iteration method is proposed, and convergence analysis of the corresponding learning control algorithm is studied. With certain assumptions, the proposed algorithm guarantees that the output of the system converges to the desired output trajectory within a finite time interval. The theoretical analysis is supported by numerical examples. The results indicate that the p-accelerated normal S-iterative learning control algorithm outperforms both the first-order PD-type iterative learning control and second-order PD-type iterative learning control algorithms for discrete linear singular systems theoretically and numerically.

Stability analysis for singular random impulsive control system: A novel neutral impulsive delay system approach

The paper studies stability analysis for an uncertain singular time varying delay system (USTDS) under random impulsive control (RIC). It also proves the stability results for a singular impulsive time delay system in terms of neutral impulsive time delay system approach. Besides, we derive the new sufficient conditions for stability results like exponential stability (ES) and robust exponential stability (RES) of the proposed system via linear matrix inequality (LMI) by employing the Lyapunov–Krasovskii functional (LKF) approach. In addition, two numerical examples, along with graphical simulations, are provided to illustrate the validity and effectiveness of the proposed results.

Finite-time stability of singular time-delay systems based on a new weighted integral inequality

In this work, we study the finite-time stability for singular time-delay systems. Particularly, we analyze the effects from the exponential weighted function eη(t−s). A new weighted integral inequality in the form of infinite series for solving finite-time stability problems has been derived. Based on that, some sufficient conditions have been obtained to guarantee that the underlying system is finite-time stable. A numerical example is provided to demonstrate the efficiency of our methods.

Stability analysis of nonlinear time-delay singular systems via improved barbălat’s lemma

This paper revisits asymptotic stability problem of nonlinear time-delay singular systems (NTDSs). Many existing stability results for this problem are derived based on the classical Barbălat’s lemma. This lemma puts two requirements on the considered functions or functionals. One is uniform continuity, the other is boundedness of the infinite integral. However, in some cases, the first requirement is difficult to be satisfied. To mitigate this limitation, a novel improved Barbălat’s lemma is proposed in some literature. In this improved lemma, the requirement of uniform continuity is relaxed by quasi-uniform continuity. By virtue of this improved Barbălat’s lemma, this paper establishes a less conservative stability theorem for NTDSs. Then, the derived results related to NTDSs are applied to investigate stability problem of linear time-delay singular systems. To demonstrate the effectiveness of the proposed results, a numerical example about circuit systems is provided.

Robust preview control of nonlinear uncertain discrete-time time-delayed singular systems via sliding mode approach

This paper addresses the problem of preview sliding mode control for a class of nonlinear uncertain discrete-time singular systems with time-delays. A difference operator approach is used to deal with the controlled system such that the derived augmented systems including preview information of reference signal can be constructed. A suitable surface is proposed in the sense of admissibility by the free-weighed matrix technique. Based on this, a sliding mode controller with preview information is constructed incorporating with the tracking error to ensure that the closed-loop control system reaches the designed sliding mode surface within finite time. To apply the proposed control scheme to the practical engineering systems, the sliding mode tracking controller with preview information is developed for a DC motor based on the proposed control approach. The comparative experiment results demonstrate that the preview information of reference signal can improve the tracking performance.

Further Improvement for Admissibility Analysis of Singular Time-Delay Systems

This article concerns the admissibility analysis of singular time-delay systems. The aim is to get superior criteria in both low conservativeness and less decision variables. To this end, the systems are decomposed and treated with different methods. The Lyapunov–Krasovskii functionals (LKFs) are constructed based on the state decomposition. By using tighter integral inequalities and the free weighting matrix method, some new admissibility criteria are derived to compare with the previous results, and are applied to the partial element equivalent circuits (PEECs) in numerical examples, by which the advantages of the proposed method are verified.

Disturbance Rejection in Singular Time-delay Systems with External Disturbances

Disturbance Rejection in Singular Time-delay Systems with External Disturbances

A variable memory state feedback and its application to robust control of uncertain singular time-delay systems

A variable memory state feedback and its application to robust control of uncertain singular time-delay systems

Admissibility Analysis and Controller Design for Discrete Singular Time-Delay Systems Embracing Uncertainties in the Difference and Systems’ Matrices

This paper mainly investigates the admissibility analysis and the admissibilizing controller design for the uncertain discrete singular system with delayed state. Based on Lyapunov–Krasovskii stability theory, an original admissibility condition for the nominal singular delay system is first presented. By involving the uncertainties in both difference and system matrices simultaneously, we devote to analyzing the robust admissibility for the regarded uncertain discrete singular system with delayed state. Furthermore, by hiring the state feedback control law, we further discuss the admissibilizing controller design for the resulting closed-loop system. Since all the derived criteria are expressed in terms of strict linear matrix inequalities (LMIs) or parametric LMIs, we thus can handily verify them via current LMI solvers. Finally, two numerical examples are given to illustrate the effectiveness and validity of the proposed approach.

Stability analysis of singular time-delay systems using the auxiliary function-based double integral inequalities

Recently, there have been a few developments reported on using the Wirtinger/free-matrix-based single integral inequality to stability problem of singular time-delay systems but there has been no report on the double ones. This paper presents an extension on applying the auxiliary function-based double integral inequality to the problem. Furthermore, an extension of the delay-dependent matrix technique into the single integral term of the Lyapunov–Krasovskii function to reduce more the conservatism has also been presented. By proposing an extended Lyapunov–Krasovskii functional (LKF) with triple integral terms and three delay-dependent matrices, a new delay-derivative-dependent stability criterion is derived. The effectiveness of the obtained result is illustrated through a numerical example.

Stability of switched singular time delay systems with switching induced state jumps

This study addresses the problem of exponential stability for switched singular state-delayed systems with switching induced state jumps, which has not been studied up to now. The considered state delay varies in a time-varying interval. On the basis of equivalent dynamics decomposition, a model of state jump at switching instants is firstly established under an assumption that the time length between arbitrary two adjacent switches is larger than the upper bound of the state delay. Then, a sufficient condition on exponential stability of the system under the reranged dwell-time switching constraint is presented. The key idea is the design of a dwell-time-dependent generalised Lyapunov function as well as a dwell-time-dependent function with respect to algebraic variables and application of the Razumikhin approach. The obtained stability condition exploits the lower bound and the upper bound of the dwell time. In addition, it is independent of the size of the state delay and allows the delay to be a fast time-varying function. Finally, two numerical examples are given to show the efficacy of the derived result.

Periodic event‐triggered and self‐triggered control of singular system under stochastic cyber‐attacks

The periodic event-triggered control (PETC) and self-triggered control (STC) for networked singular systems under denial-of-service (DoS) attack and deception attack are studied. Due to the fact that DoS attack is able to prevent the control input from transmitting and deception attack falsifies the control input as a non-linear disturbance, a closed-loop system is constructed with different control inputs based on the switched system method. Next, the attention is focused on the design of PETC and STC schemes. PETC scheme adopts the input delay approach to transform the closed-loop system into a switched singular time-delay system and adjusts the triggering intervals by the frequency and duration of cyber-attacks. STC scheme relies on a reduced-order system derived from the original singular system and utilises the current sampled information to predict the next triggering instant. Then, exponential stability criteria are derived by codesigning the triggering parameter and controller gain. Finally, a small-signal version of the structure-preserving power network model is given to demonstrate the effectiveness of the proposed methods.

Dissipativity Analysis for Singular Time-Delay Systems Via State Decomposition Method

This paper studies the dissipativity of singular time-delay systems. The objective is to derive a less conservative criterion with less computational demand. Throughout this paper, the augmented Lyapunov–Krasovskii functional (LKF) and the free-matrix-based integral inequality are used to realize less conservativeness. On the basis of these techniques, a less conservative criterion is first given. Then, by decomposing singular time-delay systems into differential equations and algebraic ones, state vectors of the systems are divided into two parts. To reduce redundant decision variables, each part of the state vectors is considered independently to construct a special augmented LKF with less decision variables. As a result, an improved criterion is deduced, and thus less conservativeness and less computational demand are achieved at the same time. Moreover, the presented state decomposition method provides a new research idea for singular time-delay systems not yet reported in the literatures. Finally, the above statements are demonstrated by a numerical example.

Low-conservative robust composite nonlinear feedback control for singular time-delay systems

A low-conservative composite nonlinear feedback controller is proposed for singular time-delay systems with time-varying delay. The proposed composite nonlinear feedback controller not only improves the transient responses of the closed-loop system but it also has less conservatism than other composite nonlinear feedback controllers. The gain of the linear part of the composite nonlinear feedback controller is obtained by precise mathematical calculation to depend not only on the upper bound of the delay but also on the delay range and rate of its changes. More advantages of the proposed composite nonlinear feedback controller are its accurate operation in the presence of actuator saturation, model uncertainties, and system singularities. The linear and nonlinear parts of the proposed controller are designed by solving a linear matrix inequality problem confirmed through a theorem using Lyapunov stability analysis. The theoretical achievements are endorsed by computer simulation through numerical and practical examples.

Comment on ‘Criteria for robust finite‐time stabilisation of linear singular systems with interval time‐varying delay’

The objective of Muoi et al. 2017 is to give a delay-dependent criterion for the considered linear singular time-delay system to be finite-time stabilisable with a state feedback controller, which is formulated in terms of linear matrix inequalities. However, this criterion is not correct, which is pointed out in this note.