On Delay-independent Stability Criteria for Linear Time-delay Systems

Several LMI representations for delay-independence stability are proposed by applying Projection Lemma and the so- called“Small Scalar Method”.These criteria realize the elimination of the products coupling the system matrices and Lyapunov matrices by introducing some additional matrices.When they are applied to robust stability analysis for polytopic uncertain systems, the vertex-dependent Lyapunov functions are allowed,so less conservative results can be obtained.A numerical example is employed to illustrate the effect of these proposed criteria.     

Further results on the delay-independent asymptotic stability of linear systems

New sufficient conditions for delay-independent asymptotic stability and decaying rale for linear systems are presented. The superiority of these results is demonstrated by comparing them to those given in the literature.     

A distributed controller approach for delay-independent stability of networked control systems

This article introduces a novel distributed controller approach for networked control systems (NCS) to achieve finite gain L₂ stability independent of constant time delay. The proposed approach represents a generalization of the well-known scattering transformation which applies for passive systems only. The main results of this article are (a) a sufficient stability condition for general multi-input-multi-output (MIMO) input-feedforward-output-feedback-passive (IF-OFP) nonlinear systems and (b) a necessary and sufficient stability condition for linear time-invariant (LTI) single-input-single-output (SISO) systems. The performance advantages of the proposed approach are reduced sensitivity to time delay and improved steady state error compared to alternative known delay-independent small gain type approaches. Simulations validate the proposed approach.     

Partial stability of large-scale systems

In this paper a theorem concerning the asymptotic partial stability for large-scale systems is given. By describing high-order systems as collections of lower order interconnected subsystems, the theorem takes the form of conditions on the interconnection structure so that asymptotic partial stability property of isolated subsystems infer the same property of the over-all system. An application is given for a problem of partial controllability in the large.     

Note on the stability of large-scale systems with delays

A stability test is proposed for large-scale systems with delays by employing both the aggregation technique and solutions of the complex Lyapunov equation. An example is given to illustrate the application of the results     

时滞非线性随机大系统的指数稳定性

建立了一般随机泛函微分方程p阶均值指数稳定与几乎必然指数稳定的新型判据, 然后应用所得判据到具有可变多时滞的非线性随机大系统, 得到了这种随机大系统时滞无关的均方指数稳定与几乎必然指数稳定的代数判据.     

Robust stability of uncertain large-scale systems with time delay

In this paper, the Lyapunov functional has been used to study the robust stability of uncertain large-scale systems with time delay; some new delay-independent conditions for stability of these uncertain large-scale systems are obtained. Finally, some examples are given to illustrate our results and to compare with previous results.     

Lotka-Volterra-like approach to large-scale systems stability

A new aggregation form of large-scale systems is proposed in this paper. It is of the ‘Lotka-Volterra’ type and appears natural for the generalized Lotka-Volterra large-scale (possibly time-varying) systems, which is shown in the paper. The Lotka-Volterra aggregation form yields a comparison system of the generalized Lotka-Volterra type, which is composed of a linear and a non-linear part. In addition this aggregation form leads to new stability conditions for time-varying large-scale systems, and enables an extension of Weissenberger's results on exponential stability domain estimates to the asymptotic stability domain estimate of time-varying systems. An advantageous feature of the system aggregation and stability analysis developed in the paper is the omission of requirements for (any particular, e.g. exponential) stability of disconnected subsystems.     

On the conjunction practical stability and controllability of large-scale impulsive control systems

We studied the conjunction practical stability and controllability of large-scale impulsive control systems by using the comparison systems and vector Lyapunov functions. Then the less conservative sufficient conditions fo r conjunction practical stability and controllability of large-scale impulsive control system were obtained.     

On the conjunction practical stability and controllability of large-scale impulsive control systems

1Introduction Asystem may be defined as a series of programs whichare designed to run sequentially.With the development ofscience,the scale of the systems with complicated structureis increasing.This causes the generationand development ofthe theory oflarge_scale system.Now,thelarge_scale systemhas become one of the important theoretic foundations ofthe systems engineering.There has been a significantdevelopment in the theory of impulsive differentialequations inthe past10years[1~3].If we wan…     

Asymptotic stability and instability of large-scale systems

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations. With minor technical adjustments, the theory is broadened to include considerations of unstable subsystems as well as instability of composite systems.     

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.     

Robust stability of linear perturbed discrete large-scale systems with saturating actuators

Robust stability conditions are considered for linear perturbed large-scale systems with saturating actuators in the discrete-time case. Both non-linear and linear perturbations are considered. Two types of controllers, a state feedback and a dynamic controller, are introduced for each sub-system to guarantee asymptotic stability of the perturbed large-scale system.     

Delay-dependent robust stability of uncertain fuzzy large-scale systems with time-varying delays

This paper addresses the stability problem of fuzzy large-scale systems (FLSSs) with uncertainties and arbitrary time-varying delays. The stability conditions, which are less conservative and more applicable than the existing results, are derived by a novel Lyapunov-Krasovskii functional method and expressed in terms of linear matrix inequalities (LMIs). Two examples are given to demonstrate the correctness and advantage of our theoretical results.     

Uniform stability of large-scale delay discrete impulsive systems

This article investigates the problem of uniform stability for the large-scale delay DIS (discrete impulsive systems). By establishing the comparison principle for the general delay DIS, uniform stability criteria are derived for three kinds (linear, affine and non-linear) of large-scale delay DIS. The obtained criteria shows that the stability properties of non-linear large-scale delay DIS can be derived by comparing to a linear and lower dimension delay DIS, with known stability properties. Some examples are given to illustrate results obtained by us.     

离散广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是广义大系统理论的基本问题之一,对其稳定性的研究要比状态空间大系统复杂得多,因为广义大系统不仅需要考虑稳定性,而且还要考虑正则性和因果性(离散广义系统)及脉冲自由(连续广义系统).本文在所有孤立子系统都是正则的且具有因果关系的条件下,利用Lyapunov方程,应用Lyapunov函数方法,研究了广义离散线性大系统和广义离散非线性大系统的稳定性和不稳定性问题,给出了离散广义大系统稳定性和不稳定性判定定理,得到了离散广义大系统的关联稳定参数域和不稳定域.     

Moment stability of linear stochastic non-triangular large-scale systems

The second-moment global exponential stability of large-scale stochastic systems is presented in this paper. The particular class of non-triangular linear parametric stochastic systems is considered. For this class, the second moments are treated as the new state space and the standard procedure of analysis of large-scale deterministic systems is applied. An example is given to illustrate the criteria.     

Multi-layer structure and stability of discrete large-scale systems

The structure of a discrete large-scale system is analyzed. It is shown that a discrete large-scale system can be considered with a multi-layer structure, each layer of which can be considered as a minimal strongly connected system (MSCS), except the highest layer which is a simply connected system. In studying the stability, a direct method is firstly presented for MSCS. Analysis and examples show that the stability criteria given here for MSCS are less conservative than those in other literature. When the isolated subsystems in each layer (which are also MSCS) are stable, the large-scale system is stable.     

Decomposition-aggregation of large-scale power systems and stability studies

In this paper the problem of transient stability of large-scale power systems is examined through decomposition-aggregation techniques. Two approaches for decomposition and reduction of dynamical models of the systems are described. Then the stability studies for the reduced models are investigated, and some of the results of application of these approaches to a practical system are reported.     

Continuous-time temporal back-propagation with adaptable timedelays

Backpropagation is extended to continuous-time feedforward networks with internal, adaptable time delays. The new technique is suitable for parallel hardware implementation, with continuous multidimensional training signals. The resulting networks can be used for signal prediction, signal production, and spatiotemporal pattern recognition tasks. Unlike conventional backpropagation networks, they can easily adapt while performing true signal prediction. Simulation results are presented for networks trained to predict future values of the Mackey-Glass chaotic signal, using its present value as an input. For this application, networks with adaptable delays had less than half the prediction error of networks with fixed delays, and about one-quarter the error of conventional networks. After training, the network can be operated in a signal production configuration, where it autonomously generates a close approximation to the Mackey-Glass signal.