Singular Time-delay Systems Research Articles

Robust stability of uncertain singular time-delay systems via LFT approach

The robust stability problem of continuous-time singular systems with multiple state delays and bounded parametric uncertainties is considered. Both commensurate and non-commensurate delays are investigated. On the basis of the linear fractional transformations (LFTs) framework and μ-analysis, a systematic approach is derived to convert the robustness problem to a robust nonsingularity problem. Some explicit conditions are proposed to guarantee the uncertain singular time-delay system being regular, impulse-free and stable independent of delay. Two illustrative examples are given to show the feasibility of the proposed technique.

On parameterized Lyapunov–Krasovskii functional techniques for investigating singular time-delay systems

The problem of robust stability of a singular time-delay system is investigated. A novel Lyapunov–Krasovskii functional (LKF) is introduced which is a singular-type complete quadratic Lyapunov–Krasovskii functional with polynomial parameters. Stability conditions are derived in the form of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and lower conservatism of the new proposed stability criterion.

Robust Exponential Admissibility of Uncertain Switched Singular Time-delay Systems

This paper investigates the problem of robust exponential admissibility for a class of continuous-time uncertain switched singular systems with interval time-varying delay. By defining a properly constructed decay-rate-dependent Lyapunov function and the average dwell time approach, a delay-range-dependent sufficient condition is derived for the nominal system to be regular, impulse free, and exponentially stable. This condition is also extended to uncertain case. The obtained results provide a solution to one of the basic problems in continuous-time switched singular time-delay systems, that is, to identify a switching signal for which the switched singular time-delay system is regular, impulse free, and exponentially stable. Numerical examples are given to demonstrate the effectiveness of the obtained results.

Delay decomposition approach to delay-dependent stability for singular time-delay systems

This study deals with the problem of delay-dependent stability analysis for singular time-delay systems. By employing the delay decomposition approach, an improved delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs), which ensures that the singular time-delay system is regular, impulse free and asymptotically stable. This stability criterion, which is obtained without using model transformation and bounding technique for cross-product terms, is much less conservative and includes some existing results as its special cases. Numerical examples are given to illustrate the effectiveness of the proposed method.

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.

Delay-dependent Stability Analysis for Discrete Singular Systems with Time-varying Delays

This paper studies the problem of stability analysis for discrete singular time delay systems. Without resorting to the decomposition and equivalent transformation of the considered system, some new delay-dependent criteria are established for the considered systems to be regular, causal, and stable in terms of linear matrix inequality (LMI) approach. The obtained criteria are less conservative, because the technique used in this paper makes more use of the information on the involved time-varying delays than the existing techniques do. A numerical example is given to illustrate the effectiveness and the benefits of the proposed methods.

Delay-dependent Stability Criteria for Singular Time-delay Systems

This note studies the problem of singular time-delay systems. At first, a simplified stability criterion is derived after establishing equivalence among several recently proposed stability criteria. By using a delay decomposition method, a new stability criterion, which is much less conservative than the existing ones, is presented. A numerical example is given to illustrate the effectiveness and less conservatism of the new proposed stability criterion.

Reliable control for a class of uncertain singular systems with interval time-varying delay

This paper is concerned with the reliable controller design problem for a class of singular systems with interval time-varying delay and norm-bounded uncertainties. A more practical model of actuator failures than outages is considered. First, by constructing a novel Lyapunov–Krasovskii functional combined with Finsler's Lemma, an improved delay-range-dependent stability criterion for the nominal unforced singular time-delay system is established in terms of linear matrix inequality (LMI). Then, based on this criterion, an LMI condition for the design of a reliable state feedback controller is presented such that, for all parameter uncertainties and actuator failures, the resultant closed-loop system is regular, impulse-free and stable. Numerical examples are proposed to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Exponential Admissibility and Dynamic Output Feedback Control of Switched Singular Systems with Interval Time-Varying Delay

This paper is concerned with the problems of exponential admissibility and dynamic output feedback (DOF) control for a class of continuous-time switched singular systems with interval time-varying delay. A full-order, dynamic, synchronously switched DOF controller is considered. First, by using the average dwell time approach, a delay-range-dependent exponential admissibility criterion for the unforced switched singular time-delay system is established in terms of linear matrix inequalities (LMIs). Then, based on this criterion, a sufficient condition on the existence of a desired DOF controller, which guarantees that the closed-loop system is regular, impulse free and exponentially stable, is proposed by employing the LMI technique. Finally, some illustrative examples are given to show the effectiveness of the proposed approach.

Observer-based resilient L 2 – L ∞ control for singular time-delay systems

The problem of non-fragile (or resilient) L2–L∞ control for a class of singular systems with time-varying delay is considered via observer-based state feedback control. The objective is to design an observer-based feedback controller with additive gain variations such that, for all admissible observer and controller gain variations, the closed-loop system is regular, impulse free and stable with a prescribed L2–L∞ performance index satisfied. In terms of linear matrix inequalities, a new delay-dependent stability criterion is derived. Based on the obtained criterion, the non-fragile observer and controller design method is proposed. Numerical example and simulation results are included to show the effectiveness of the proposed results.

Improved Results on Delay-dependent <I>H</I><SUB>∞</SUB>Control for Singular Time-delay Systems

摘要: 讨论广义时滞系统的时滞依赖控制问题. 基于线性矩阵不等式(LMI)方法和增广Lyapunov泛函, 给出保证系统正则、无脉冲、稳定且满足性能指标的时滞依赖有界实引理. 在此引理的基础上, 给出基于严格LMI的状态反馈控制器存在的时滞依赖条件. 同时给出所需状态反馈控制器的明确表示. 数值例子表明本文的结果改进了已有结论的保守性. 关键词: 广义系统 / 时滞系统 / 时滞依赖 / 控制 / 线性矩阵不等式

Exponential stability and static output feedback stabilisation of singular time-delay systems with saturating actuators

This study deals with the class of continuous-time singular linear systems with time-varying delays. The stability and stabilisation problems of this class of systems are addressed. Delay-range-dependent sufficient conditions such that the system is regular, impulse free and α-stable are developed in the linear matrix inequality (LMI) setting and an estimate of the convergence rate of such stable systems is also presented. An iterative LMI (ILMI) algorithm to compute a static output feedback controller gains is proposed. Some numerical examples are employed to show the usefulness of the proposed results.

Delay-dependent L2- L∞ Filter for Singular Time-delay Systems

The problem of L 2- L ∞ filtering is discussed for singular time-delay systems. Attention is focused on the design of full-order filter that guarantees the delay-dependent exponential admissibility and a prescribed noise attenuation level in L 2- L ∞ sense for the filtering error dynamics. The desired filter can be constructed by solving certain linear matrix inequality (LMI). Numerical examples are given to show that the methods have less conservatism.

H∞ filter design for singular time-delay systems

This paper aims to solve the H∞ filtering problem for singular time-delay systems. Two new and improved delay-dependent bounded real lemmas (BRLs), which are equivalent to each other, are proposed. Based on one of them, an H∞ filter is designed via a linear matrix inequality (LMI) approach. Numerical examples are given to illustrate that the newly proposed methods introduce less conservatism than the existing ones.

Improved Results on Delay-dependent H∞ Control for Singular Time-delay Systems

The problem of delay-dependent H ∞ control for singular systems with state delay is discussed. In terms of linear matrix inequality (LMI) approach, a delay-dependent bounded real lemma (BRL) is presented to ensure the system to be regular, impulse free, and stable with H ∞ performance condition via an augmented Lyapunov functional. Based on the BRL obtained, the delay-dependent condition for the existence of H ∞ state feedback controller is presented via strict LMI. An explicit expression for the desired state feedback controller is also given. Numerical examples are presented to illustrate the significant improvement on the conservativeness of some reported results in the literature.

Passivity-based sliding mode control of uncertain singular time-delay systems

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

Delay-Dependent Robust H ∞ Admissibility and Stabilization for Uncertain Singular System with Markovian Jumping Parameters

This paper investigates the problem of delay-dependent robust H ? admissibility and stabilization for uncertain singular time delay systems with Markovian jumping parameters. The considered systems are not necessarily assumed to be regular and impulse-free. In terms of the linear matrix inequality (LMI) approach, a delay-dependent stochastic admissibility criterion is given to ensure that the nominal system is regular, impulse-free and stochastically stable. Based on this criterion, the problem is solved. A numerical example is provided to demonstrate the efficiency of the proposed methods in this paper.

Lyapunov–Krasovskii functional for uniform stability of coupled differential-functional equations

This article discusses the Lyapunov–Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov–Krasovskii functional is established. Discretization is used to render the stability criterion to an LMI form.

Variable structure control of linear time-delay uncertain singular system

Synthesis and designing of variable structure controller for time-delay singular uncertain system are studied. Firstly, the system is decomposed into two low dimensional subsystems. Secondly, switching function and variable structure controller are designed with regard to uncertain part of the system satisfies matching conditions or not. The designing guarantee the movement of the system in switching manifolds is asymptotically stable and the variable structure controller can force trajectory of the system to arrive at the switching manifold in finite time. Finally, a numerical example and its simulation figure are given to demonstrate feasibility and validity of the design method.

Delay-dependent dissipativity of singular time-delay systems

Delay-dependent dissipativity of singular time-delay systems