Analysis Of Singular Systems Research Articles

Passivity Analysis of Singular Neural Systems with Variable Delays

In this paper, some sufficient conditions for singular Hopfield neural networks (SHNNs) with variable delays to be passive are presented. The passivity of delayed singular Hopfield neural networks without uncertainties is studied, and then the result is extended to the case with time-varying parametric uncertainties. The results are based on a Lyapunov functional construction. Numerical examples are also given to demonstrate the effectiveness of the theoretical results. In addition, these criteria possess important leading significance in design and applications of passivity analysis of SHNNs with variable delays.

New results on stability analysis of singular time-delay systems

ABSTRACTThis paper deals with the problem of delay-dependent stability analysis for singular systems with a constant time delay. By employing the Jensen inequality and the Wirtinger-based inequality, new delay-dependent stability criteria are developed. Furthermore, in order to obtain less conservative results, a new method of constructing Lyapunov--Krasovskii functionals (LKFs) is used. It should be pointed out that the positive-definiteness restrictions on some symmetric matrices of the LKFs are removed. All the criteria are proposed in terms of strict linear matrix inequalities. Finally, numerical examples are given to demonstrate the less conservatism of the results.

Dissipativity analysis for discrete singular systems with time-varying delay

In this paper, the issue of dissipativity analysis for discrete singular systems with time-varying delay is investigated. By using a recently developed inequality, which is less conservative than the Jensen inequality, and the improved reciprocally convex combination approach, sufficient criteria are established to guarantee the admissibility and dissipativity of the considered system. Moreover, H∞ performance characterization and passivity analysis are carried out. Numerical examples are presented to illustrate the effectiveness of the proposed method.

Admissibility analysis for linear singular systems with time-varying delays via neutral system approach

This paper studies the admissibility problem for a class of linear singular systems with time-varying delays. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, an appropriate type of Lyapunov–Krasovskii functionals is proposed to develop a delay-derivative-dependent admissibility condition in terms of linear matrix inequalities. The derivation combines the Wirtinger-based inequality and reciprocally convex combination method. The present criterion is also for the stability test of retarded and neutral systems with time-varying delays. Some examples are provided to illustrate the effectiveness and the benefits of the proposed method.

Robust stability analysis and stabilisation of uncertain neutral singular systems

ABSTRACTThis paper studies the problem of robust stability and stabilisation of uncertain neutral singular systems and develops a new stability criterion of the differential operator, ℑ by the final value theorem for Laplace transform. By utilising Lyapunov functional and free-weight matrix method, we employ the linear matrix inequality technique and the stability condition to derive some new criteria which ensure the robustly asymptotical stability of the studied system. State feedback controllers with disturbance are designed to guarantee the robustly asymptotical stability of the uncertain system. Numerical examples are provided to validate the effectiveness of the obtained results.

Admissibility analysis for discrete-time singular systems with randomly occurring uncertainties via delay-divisioning approach

This paper deals with the problem of admissibility analysis for discrete-time singular system with time-delays. The uncertainties occurring in the system parameters are assumed to be random. By constructing Lyapunov functional, sufficient delay-dependent stochastic admissibility conditions are established via delay divisioning approach in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. Numerical examples and their simulation results are given to illustrate the effectiveness of the obtained theoretical results.

Admissibility analysis for discrete-time singular systems with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the lower and upper delay bounds. Finally, numerical examples are provided to substantiate the theoretical results.

New admissibility analysis for discrete singular systems with time-varying delay

In this paper, the issue of admissibility for discrete singular systems with time-varying delay is addressed. The main contribution of this paper is to reduce the conservatism of the considered system by adopting an improved reciprocally convex combination approach to bound the forward difference of the double summation term, and utilizing the reciprocally convex combination approach to bound the forward difference of the triple summation term in the Lyapunov function. Without employing decomposition and equivalent transformation of the considered system, a strict delay-dependent linear matrix inequality (LMI) criterion is built to guarantee the considered system to be regular, causal and stable. A numerical example is given to illustrate the effectiveness of this proposed method.

State analysis of time-varying singular nonlinear systems using Legendre wavelets

In this paper, the Legendre wavelet method for State analysis of time-varying singular nonlinear systems is studied. The properties of Legendre wavelets and its operational matrices are first presented and then are used to convert into algebraic equations. Also the convergence and error analysis for the proposed technique have been discussed. Illustrative examples have been given to demonstrate the validity and applicability of the technique. The efficiency of the proposed method has been compared with Haar wavelet method and it is observed that the Legendre wavelet method is more convenient than the Haar wavelet method in terms of applicability, efficiency, accuracy, error, and computational effort.

Finite-time stability analysis of fractional singular time-delay systems

This paper studies the finite-time stability of fractional singular time-delay systems. First, by the method of the steps, we discuss the existence and uniqueness of the solutions for the equivalent systems to the fractional singular time-delay systems. Furthermore, we give the Mittag-Leffler estimation of the solutions for the equivalent systems and obtain the sufficient conditions of the finite-time stability for the original systems.

Distributed admissible consensus control for singular swarm systems with switching topologies

Summary The interaction topologies of swarm systems may be time varying due to the motions of agents or the failure of communication equipment. The current paper focuses on admissible consensus analysis and design problems for singular swarm systems with switching topologies. Admissible consensus analysis problems are converted into admissible ones of a reduced-order switching subsystem by the state projection on the consensus subspace and the complement consensus subspace. Furthermore, an approach to determine the consensus function is proposed by the first equivalent form. Moreover, by the Riccati equation, admissible consensus design criteria are presented, which can guarantee the scalability of singular swarm systems because they are independent of the number of agents. Finally, numerical examples are presented to check the correctness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

RobustH∞performance analysis for uncertain discrete-time singular systems with time-varying delays

This paper considers the problem of robust H∞ performance analysis for uncertain discrete-time singular systems with time-varying delays. Firstly, a delay-dependent stability criterion under the H∞ performance index for the systems is given based on constructing a generalized Lyapunov–Krasovskii function and introducing a new difference inequality. Then, a sufficient condition ensuing the system to be regular, causal as well as stable for all admissible uncertainties is proposed in terms of a set of strict linear matrix inequalities (LMIs). Finally, we provide examples to show the reduced conservatism and effectiveness of the proposed conditions. Copyright © 2014 John Wiley & Sons, Ltd.

A delay decomposition approach to [formula omitted] admissibility for discrete-time singular delay systems

This paper considers the problem of delay-dependent admissibility condition and H∞ performance analysis for discrete-time singular delay systems. By utilizing the delay decomposition approach, an improved delay-dependent admissibility condition is presented in terms of linear matrix inequalities (LMIs). This admissibility condition is much less conservative than some existing results and includes those as its special cases. Based on the proposed condition, a new delay-dependent bounded real lemma is also given, which guarantees the admissibility and the H∞ performance. Numerical examples are given to illustrate the effectiveness of the proposed method.

Admissible [formula omitted] consensus for singular time-delayed swarm systems with external disturbances

Admissible consensus analysis and design problems for high-order linear time-invariant singular swarm systems with time delays and external disturbances are investigated. Firstly, by the state space decomposition, a necessary and sufficient condition for admissible consensus is given and an approach is presented to determine consensus functions on the basis of different impacts of initial states of agents and external disturbances, which describe the absolute motions of singular swarm systems as a whole. Then, an L2 evaluation approach which requires fewer limitations on the structures of consensus functions is proposed to determine the influences of external disturbances on relative motions among agents, and linear matrix inequality criteria for admissible L2 consensus and consensualization are shown. Finally, numerical simulations are presented to demonstrate theoretical results.

Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

A Delay Decomposition Approach to the Stability Analysis of Singular Systems with Interval Time-Varying Delay

This paper investigates delay-dependent stability problem for singular systems with interval time-varying delay. An appropriate Lyapunov-Krasovskii functional is constructed by decomposing the delay interval into multiple equidistant subintervals, where both the information of every subinterval and time-varying delay have been taken into account. Employing the Lyapunov-Krasovskii functional, improved delay-dependent stability criteria for the considered systems to be regular, impulse-free, and stable are established. Finally, two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Positivity of discrete singular systems and their stability: An LP-based approach

In this paper we present an efficient approach to the analysis of discrete positive singular systems. One of our main objectives is to investigate the problem of characterizing positivity of such systems. Previously, this issue was not completely addressed. We provide easily checkable necessary and sufficient conditions for such problem to be solved. On the other hand, we study the stability of discrete positive singular systems. Note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone. All the conditions we provide are necessary and sufficient and are based on a reliable computational approach via linear programming.

Interpreting nonstationary environmental cycles as amplitude-modulated (AM) signals

Inspired by an analogy to AM radio signals, amplitude modulation (AM) is proposed here as a useful view of nonstationary environmental periodicities, and applied to hydrologic and air quality datasets. Both example time series considered exhibit seasonally evolving diel cycles, with large (small) daily cycle amplitudes in summer (winter). The carrier wave is taken to be a sinusoidal daily cycle; this is multiplied by an information signal consisting of a sinusoidal annual cycle, forming an envelope to the diel variations. Our results suggest that amplitude modulation may offer a novel, compact, and accessible perspective, both qualitatively and quantitatively, on the net phenomenological behaviour arising from highly complex, nonlinear, and diverse environmental process dynamics. Physical interpretations, synergies with common environmental time series processing or analysis methods (Kolmogorov-Zurbenko filtering, classical spectral analysis, and singular systems analysis), and potential future research directions are also explored.

Stability analysis and optimal control of stochastic singular systems

In this paper, problems of stability and optimal control for a class of stochastic singular systems are studied. Firstly, under some appropriate assumptions, some new results about mean-square admissibility are developed and the corresponding LMI sufficient condition is given. Secondly, finite-time horizon and infinite-time horizon linear quadratic (LQ) control problems for the stochastic singular system are investigated, in which the coefficients are allowed to be random in control input and quadratic criterion. Some results involving new stochastic generalized Riccati equation are discussed as well. Finally, the proposed LQ control model for stochastic singular systems provides an appropriate and effective framework to study the portfolio selection problem in light of the recent development on general stochastic LQ problems.

Delay-dependent dissipative control for stochastic singular systems with state delay

Abstract The problem of delay-dependent dissipative analysis and control for stochastic singular systems with state delay is investigated in this paper. Delay-dependent dissipative condition for the stochastic singular systems with state delay is obtained by employing singular stochastic Lyapunov and LMI-based methods. Based on this condition, a delay-dependent dissipative controller is presented. A numerical example is provided to demonstrate the effectiveness of the proposed approach.