Singular Time-delay Systems Research Articles

Stability of singular time-delay systems in the sense of non-Lyapunov: Classical and modern approach

This paper provides sufficient conditions for both practical stability and finite-time stability of linear singular continuous time-delay systems which can be mathematically described as Ex(t)=Aox(t)+A1x(t-t). Considering a finite-time stability concept, new delay independent and delay dependent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior. Moreover an linear matrix inequality (LMI) approach has been applied in order to get less conservative conditions.

Robust Stability and Stabilization for Singular Time-Delay Systems with Linear Fractional Uncertainties: A Strict LMI Approach

This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs), delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

Novel Observer-Based Suboptimal Digital Tracker for a Class of Time-Delay Singular Systems

This paper presents a novel suboptimal digital tracker for a class of time-delay singular systems. First, some existing techniques are utilized to obtain an equivalent regular time-delay system, which has a direct transmission term from input to output. The equivalent regular time-delay system is important as it enables the optimal control theory to be conveniently combined with the digital redesign approach. The linear quadratic performance index, specified in the continuous-time domain, can be discretized into an equivalent decoupled discrete-time performance index using the newly developed extended delay-free model. Additionally, although the extended delay-free model is large, its advantage is the elimination of all delay terms (which included a new extended state vector), simplifying the proposed approach. As a result, the proposed approach can be applied to a class of time-delay singular systems. An illustrative example demonstrates the effectiveness of the proposed design methodology.

Containment analysis and design for high-order linear time-invariant singular swarm systems with time delays

Containment analysis and design problems for high-order linear time-invariant singular swarm systems with time delays on directed graphs are dealt with. To eliminate impulse terms in singular swarm systems and ensure that the singular swarm systems can achieve containment, time-delayed protocols are presented for leaders and followers respectively. By model transformation, containment problems of singular swarm systems are converted into the asymptotically stable problems of multiple low-dimensional time-delayed systems. In terms of linear matrix inequality, sufficient conditions are presented for time-delayed singular swarm systems to achieve containment, which are independent of the number of agents. By applying changing variable methods, an approach is provided to determine the gain matrix in the protocols. Numerical simulations are shown to demonstrate theoretical results.

Robust stability and stabilization of uncertain discrete singular time-delay systems based on PNP Lyapunov functional

Robust stability and stabilization of uncertain discrete singular time-delay systems based on PNP Lyapunov functional

Exponential stability of hybrid switched nonlinear singular systems with time-varying delay

We address exponential stability of switched nonlinear singular systems with time-delay in which delay is time varying and presents in the states. For switched nonlinear singular time-delay systems with average dwell-time switching signals, we provide sufficient conditions, in terms of linear matrix inequalities (LMIs) to guarantee the exponential stability of such systems. By using Lyapunov–like Krasovskii approach, the relationship between the average dwell-time of the switched nonlinear singular time-delay system and the exponential decay rate of differential and algebraic states is given. A numerical example is also included to illustrate the effectiveness of the results proposed in this paper.

Delay-dependent admissible consensualization for singular time-delayed swarm systems

Admissible consensus analysis and design problems for high-order linear time-invariant singular swarm systems with time delays are investigated. Firstly, by state decomposition, the admissible consensus problem is transformed into admissible problems of multiple singular subsystems with lower dimensions. Then, linear matrix inequality (LMI) criteria for admissible consensualization are presented, which only involve eight LMI constraints independent of the number of agents. Moreover, an explicit expression of the consensus function which is independent of time delays is presented, and the impacts of protocol states and interaction topologies on the consensus function are revealed. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.

Exponential mean-square stability of time-delay singular systems with Markovian switching and nonlinear perturbations

This paper considers exponential stability in mean-square of singular Markovian jump systems. The systems under consideration involve nonlinear perturbation and time-varying delays. By using the Lyapunov–Krasovskii functional, delay-dependent stability conditions in terms of linear matrix inequality (LMI) are addressed, which guarantee exponential mean-square stability and a prescribed H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness of the proposed main results.

Passivity-based Sliding Mode Control of Uncertain Nonlinear Singular Time-delay Systems Subjected to Input Nonlinearity

Passivity-based Sliding Mode Control of Uncertain Nonlinear Singular Time-delay Systems Subjected to Input Nonlinearity

Stability and stabilization for discrete-time singular systems with infinite distributed delays and actuator failures

In this paper, a reliable H∞ controller is designed for discrete-time singular systems with infinite distributed delays. Firstly, a stability criterion is obtained based on linear matrix inequality (LMI). Then a controller is designed to ensure the singular time-delay system to be regular, causal and stable with disturbance attenuation level γ for possible actuator failures. A numerical example is given to illustrate the validity of the proposed approach.

Sliding mode control with bounded [formula omitted] gain performance of Markovian jump singular time-delay systems

In this paper, we investigate the problem of sliding mode control (SMC) of Markovian jump singular time-delay systems. The aim is to consider the bounded ℒ2 gain performance in the analysis of sliding mode dynamics, thus to improve the transient performance of the SMC system. Firstly, a delay-dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded ℒ2 gain performance condition. 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 singular Markovian jump time-delay system. Then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived. Moreover, an SMC law is 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 techniques.

Delay-Dependent Stabilization for Singular Time-Delay Systems

Some new results of delay-dependent stabilization for linear singular time-delay systems are presented. And the time delay considered here is assumed to be constant but unknown. By using a new Lyapunov-krasovskii functional which splits the whole delay interval into two subintervals and defines a different energy function on each subinterval, a sufficient delay-dependent condition is obtained for the singular time-delay system to be regular, impulse free and stable.

Optimal Control for Time Delay Singular Systems

For the class of singular time-delay dynamical systems we present optimal control results. We developed unified framework for feedback optimal and inverse optimal control involving a nonlinear-nonquadratic performance functional. It is shown that the cost functional can be evaluated in closed-form as long as the cost functional considered is related in a specific way to an underlying Lyapunov function that guarantees asymptotic stability of the nonlinear closed-loop singular time-delay system. Furthermore, the Lyapunov function is shown to be a solution of a steady-state, Hamilton-Jacobi-Bellman equation.

Stabilization of discrete-time switched singular time-delay systems under asynchronous switching

This paper is concerned with the problem of state feedback stabilization of a class of discrete-time switched singular systems with time-varying state delay under asynchronous switching. The asynchronous switching considered here means that the switching instants of the candidate controllers lag behind those of the subsystems. The concept of mismatched control rate is introduced. By using the multiple Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence of a class of stabilizing switching laws is first derived to guarantee the closed-loop system to be regular, causal and exponentially stable in the presence of asynchronous switching. The stabilizing switching laws are characterized by a upper bound on the mismatched control rate and a lower bound on the average dwell time. Then, the corresponding solvability condition for a set of mode-dependent state feedback controllers is established by using the linear matrix inequality (LMI) technique. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

State Estimation for Discrete-Time Singular Jump Systems with Non-Accessible Mode Information

The mode information of Markovian jumping systems is always not accessible due to unexpected phenomenon such as data packet losses in networked control systems. It is thus extremely desirable to develop mode-independent filtering techniques for Markovian jumping systems. In this paper, a new mode-independent filtering design strategy is presented for a class of discrete-time singular time-delay systems with Markovian jumping parameters. Sufficient conditions are established so that the derived error system is regular, causal and stochastically stable with a prescribed H∞ performance level. In addition, it is illustrated that the proposed results are less conservative numerically than those in the references. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed approaches.

An LMI approach to -stability and -stabilization of linear discrete singular systems with state delay

Abstract The problems of D -stability and D -stabilization for linear discrete singular systems with state delay are addressed in this paper. By using the state augmentation technique, a necessary and sufficient D -stability condition and a sufficient D -stabilization condition for linear discrete singular time-delay systems are firstly proposed. Then, based on these conditions, quadratic D -stability and D -stabilization conditions for linear discrete singular time-delay systems with norm-bounded uncertainties and interval uncertainties are obtained, respectively. Both the D -stability and D -stabilization conditions are proposed in terms of linear matrix inequalities. Finally, illustrative examples show that the proposed conditions are effective to check the D -stability and to design the D -stabilizing controller for linear discrete singular time-delay systems.

Dissipative control for singular Markovian jump systems with time delay

SUMMARY This paper focuses on the problem of dissipative control for continuous-time singular time-delayed systems with Markovian jump parameters. Different from usually mode-dependent or mode-independent controller design methods, a partially mode-dependent dissipative controller is firstly proposed via using a mode-dependent Lyapunov function. The stochastic property of the mode available to a controller operation is taken into consideration in the corresponding controller design. Moreover, the existence of the established controller is given in terms of strict linear matrix inequalities. Finally, numerical examples are used to demonstrate the effectiveness of the given theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.

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.

H∞ control of singular time-delay systems via discretized Lyapunov functional

Abstract This paper addresses the problem of robust H ∞ control for uncertain continuous time singular systems with state delays. A new singular-type complete quadratic Lyapunov–Krasovskii functional (LKF) is introduced, which combines with the discretization LKF method to synthesis problems. An improved bounded real lemma (BRL) is presented to ensure the system to be regular, impulse free and stable with H ∞ performance condition. Based on the BRL, a memoryless state feedback controller is designed via linear matrix inequalities (LMIs), which greatly reduces the disturbance attenuation level. Numerical examples are given to illustrate improvements over some existing results.

Robust passive control for a class of singular time-delay systems with uncertainties

In the paper, the notion of passive uncertainties is proposed for uncertain singular systems under the state space. The robust passive control problem for a class of singular time-delay systems with uncertainties is discussed by using the linear matrices inequalities (LMIs), the sufficient condition of strictly passivation is obtained, and the robust passive controller for this class of uncertain singular systems is given. Finally, the feasibility of the theorems is shown by the numerical example.