Stability Of Large-scale Systems Research Articles

Stability of Large Scale Systems with Interval Coefficients

Stability determination for large scale dynamic systems with interval coefficients is studied in this paper. The main method are comparison principle and vector Lyapunov function. For delay system with interval coefficients, stability criteria independent of delays are given and model aggregation of high-order system is accomplished in stability analysis. By these criteria, one can determine stability of a large scale system from an aggregation model irrespective of whether each isolate subsystem is stable or not-Obtained low-order aggregation models for large scale and interval systems are with certain coefficients instead of interval ones. Applications to three examples show that proposed stability criteria are explicit and helpful.

Optimization of Interconnecting Parameters Regions of Stability for Large-scale Systems

In this paper, it has been proposed by the authors optimization of interconnecting parameters regions of stability for large-scale systems. Making use of the method of weighted sum type of Lyapunov function, the optimization of interconnecting parameters regions of stability has been realized on the 2-order linear constant composite system. At the same time, it has been obtained some interconnecting parameters regions of stability of n-order linear and nonlinear constant large-scale systems.

Stabilization of large-scale systems with non-linear perturbations via local feedback

The problem of robust stability for large-scale systems made of several non-linearly perturbed subsystems is considered. A stabilizing local state feedback is applied to each subsystem and the bound of permissible perturbations in each subsystem is obtained. The derived results are also applicable to the case when the perturbation in each subsystem is non-linear and time-varying. Finally, the relation between the perturbation and the local control law is established.

Stability of Volterra integrodifferential systems

The purpose of this paper is to use a decomposition-aggregation method and Liapunov functionals to discuss the stability of large scale systems described by liner Volterra integrodifferential equations.

The use of high-order forms in stability analysis

A method is proposed for determining whether forms of arbitrary high order are positive or negative definite in a region of R n coinciding with one of the coordinate angles. Using such functions, one can then establish various modifications of well-known results of stability theory. A theorem of Grujic /1/ concerning the exponential stability of large-scale systems, generalized to the case of m-th order estimates, yields new zones of absolute stability for the equations of translational motion of an aircraft. Various results are established pertaining to the monotone stability of systems in which the right-hand side is a polynomial of a special kind. In many problems of stability theory it suffices to construct a Lyapunov function which is positive or negative definite not in the whole space but only in a subspace, namely, a cone. This is a logical approach, for example, in relation to biological communities, since the trajectories of a system describing the dynamics of such interactions never leave the first orthant. Conditions for quadratric forms to be positive (negative) definite in a specific cone - one of the coordinate angles - were studied in /2/. A criterion for a quadratic form to be positive (negative) definite in a certain region of R n , similar in a sense to the conditions obtained in /2/, was established in /3/ and /4/. Even before that, a criterion was proposed /5/ for a form of order 3 to be positive (negative) definite in one of the coordinate angles. Also worthy of mention is a method described in /6/ to determine whether forms of arbitrary even order are definite in the whole space. Relying on the concept of a cone coinciding with a coordinate angle, as well as the results and /5/ and /6/, a method can be devised to investigate whether a form of arbitrary high (including odd) order is definite in an orthant of R n .

On the existence of periodic solutions for large-scale systems

In recent ten years or more, many scholars have engaged in the investigation concerning the stability of large-scale systems, but up to the present, the problem on the existence of periodic solutions for large-scale systems has yet been seldomly touched upon in the literature.

Stabilization of large-scale systems via observer–controller compensators: frequency domain approach

This paper is concerned with the stabilization or large-scale systems via an observer–controller compensator. The overall system is considered as a decentralized form containing many linear time-invariant multivariable subsystems. Using both the M-matrix property and analysis of the input-output stability, a new stability criterion for large-scale systems controlled by observer–controller compensators is derived. Finally, based on this stability criterion, a design algorithm is proposed for finding a stabilizing observer–controller compensator for large-scale systems.

State estimation of large-scale systems

This paper addresses the problem of the robustness of a Luenberger observer applied to a given large-scale system to obtain the state estimation from the viewpoint of decentralized observation. While the large-scale system suffers parametric perturbations, a robust stability criterion for decentralized state estimation and control is derived. If saturating actuators are employed to drive the large-scale system, a new stability criterion is also given for the stabilization of large-scale systems by decentralized Luenberger observer-based constrained control. Finally, the results from several simulations are provided for illustration.

Stability of large-scale systems with saturating actuators

This paper is concerned with the stability problem of a large-scale system made of J subsystems. Each subsystem contains a saturating actuator, a linear time-invariant plant, and a linear time-invariant controller. A sufficient stability condition is given for the large-scale system with saturating actuators and an algorithm for synthesizing the stabilizing controllers is proposed. The plant of each subsystem is not constrainted to be stable and/or minimum-phase.

Connective stability for large scale systems described by functional differential equations

The decomposition-aggregation method, the comparison principle, and vector Lyapunov functionals are used to investigate the stability of large-scale systems described by functional differential equations under structural perturbations. Some sufficient conditions are given so that the zero solution is connectively and uniformly asymptotically stable. An example to illustrate the main results is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An Observer Theory for Decentralized Control of Large-Scale Interconnected Systems

An observer theory is presented for decentralized stabilization of large-scale systems composed of interconnected subsystems, where the information structure constraint is conformable to subsystems. The major trouble in estimating the state of a subsystem or its linear function using a locally associated observer, is that the behavior of the subsystem is influenced by other subsystems through interconnections, but no information about the influence is communicated to the local observer. In this paper, we consider the influences as unmeasurable disturbances to subsystems, and propose to apply almost disturbance decoupling observers decentrally to estimate approximately the control inputs generated by local state feedback laws. The existence condition of such observers is provided. It is shown that the approximate estimates of local state feedback control inputs can serve for the real state feedback in decentralized stabilization problems.

Stability of Large Scale Systems Under Decentralized Control

The problem dealt with in this paper is the decentralized stabilization of linear continuous-time large scale systems (LSS) by static state feedbacks. The suggested approach consists in an additional decomposition of the local subsystems, usage of bounds on the solution of Lyapunov matrix equation, vector Lyapunov function and the comparison principle. Our main purpose is to overcome two important shortcomings of the existing approaches: the requirement for solution of Riccati (Lyapunov) matrix equations at each iteration, which may be time consuming and the a priori unawareness of this solution, involved in the stability condition. The main result is a sufficient stability condition, whose outstanding feature is flexibility. The validity of the approach and its capabilities are illustrated on the error regulation problem of a string of moving vehicles.

Nonlinear comparison systems and the stability of large-scale systems

Nonlinear comparison systems and the stability of large-scale systems

ON THE STABILITY OF LARGE-SCALE INTERCONNECTED SYSTEMS

In this paper we study the stability of large-scale systems. We consider those systems which may be viewed as an interconnection of lower order subsystems. Lyapunov stability results were considered using norm type function, which led to the use of the measure of a matrix to analyze the stability. The resultant test matrix is an M-matrix with entries that are expressed in terms of the stability properties of the subsystems and in terms of the qualitative properties of the system interconnecting structure.

Note on the stability of large-scale systems with delays

Abstract 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

Investigation of stability of large-scale systems on the basis of Lyapunov's matrix functions

Investigation of stability of large-scale systems on the basis of Lyapunov's matrix functions

Asymptotic behaviour for some large-scale systems with infinite delay

Abstract The aggregation-decomposition method is used to derive sufficient conditions for stability of large-scale systems with infinite delays under structural perturbations described by functional differential equations with finite lags appearing only in the interconnections. Electrical networks consisting of transmission lines interconnected with lumped linear and memoryless nonlinear elements can be represented by the dynamical systems considered in this paper.

STABILITY ANALYSIS OF LARGE-SCALE SYSTEMS WITH MULTIPLE DELAYS

This paper is concerned with the stability analysis of a class of linear time-invariant large-scale systems with multiple delays. By using the properties of ▪ matrices, a sufficient condition of absolute stability is first derived for low order systems described by differential-difference equations. Then a comparison theorem is presented for differential-difference inequalities. Finally, a sufficient condition of absolute stability for large-scale systems with multiple delays is established by using the aggregation technique based on vector Lyapunov functions. A numerical example is also given to illustrate the applicability of the stability criterion obtained in this paper.

A Novel Excitation Control Design for Multimachine Power Systems

This paper presents a generalized excitation control design that ensures not only a desired damping of the critical electro-mechanical modes of oscillation but also the zeroing of the terminal voltage error independent of terminal voltage excursions. The excitation system consists of a compensation transfer function utilizing the machine speed or terminal frequency and/or electrical power. A comparison of the proposed design with a conventional excitation system control indicated its effectiveness in enhancing small scale as well as large scale system stability.

A Novel Excitation Control Design for Multimachine Power Systems

This paper presents a generalized excitation control design that ensures not only a desired damping of the critical electromechanical modes of oscillation but also the zeroing of the terminal voltage error independent of terminal voltage excursions. The excitation system consists of a compensation transfer function utilizing the machine speed or terminal frequency and/or electrical power. A comparison of the proposed design with a conventional excitation system control indicated its effectiveness in enhancing small scale as well as large scale system stability.