Stability Of Large-scale Systems Research Articles

Robust decentralized stabilization of large-scale systems via eigenstructure assignment

In this paper, the problem of achieving robust stability for linear large-scale systems by decentralized feedback is considered. Sufficient conditions for stability of closed-loop system are introduced. By appropriately assigning the eigenstructure of each isolated subsystem via output feedback or state feedback, these conditions are satisfied. Based on the eigenstructure assignment result and the matrix eigenvalue sensitivity theory, a method for decentralized robust stabilization is presented.

A Novel Method for Decentralized Robust Exponential Stabilization of Large-Scale Systems

Abstract A novel approach to the design of decentralized controllers for large-scale systems by dynamic/static output state feedback is presented. A new formulation of the interaction which introduces some degrees of freedom into the design procedure is offered. Sufficient conditions for exponential stability with desirable rate of decay and maximal robustness to unstructured uncertainties in the controller and plant parameters are established. The derived conditions are generic, applicable to nonsquare and nonminimum-phase systems, and independent of the number of system states, inputs and outputs. Based on minimal sensitivity design of isolated subsystems, an analytical method for the satisfaction of the aforementioned sufficient conditions is presented. To this end, through eigenstructure assignment, compact-form sufficient conditions for minimal sensitivity are derived. Illustrative examples are presented to demonstrate the effectiveness of the proposed methodology. Genetic algorithm is employed in th...

Some Results of Developing Classical and Modern Theories of Stability of Motion

The paper presents some results obtained at the Department of Stability of Processes of the Institute of Mechanics of the NASU in the following areas: the nonclassical theories of stability of motion, the method of integral inequalities, the comparison method, stability of large-scale systems, stability analysis of motions in nonlinear mechanics, matrix-valued Lyapunov functions and their application, and qualitative analysis of population evolution. The characteristic features of the development of stability theories at the end of the 20th century are discussed in the final section

Decentralized stabilization of large scale systems with multiple delays in the interconnections

In this paper, the problem of robust stabilization of a class of time-varying large scale systems subject to external disturbances, uncertain parameters and multiple time-varying delays in the interconnections and non-linear inputs is considered. Linear memory less controllers are developed to guarantee that all solutions of the class of systems considered are uniformly ultimately bounded. Also, non-linear memoryless controllers are synthesized to guarantee that the solutions are uniformly ultimately bounded with respect to a bound with any prespecified convergence rate towards it. Finally, an example is included to illustrate the results developed in this paper.

Polytopic Connective Stability

The purpose of this paper is to consider connective stability of large scale systems when the interconnection matrices are allowed to move within a convex polytope. Distinct sets of sufficient vertex conditions are derived for polytopic connective stability in terms of convex M-matrices. A brief overview of the literature on the connective stability concept is provided, because of its relevance in stability analysis of hybrid systems.

Robust Stability of Large-Scale Systems with Aftereffect

This article is devoted to the robust stability analysis of large-scale systems involving both discrete and distributed delays. Here, the robustness property is relative to uncertainties on the time-delay function as well as on model parameters. Differential inequalities and comparison principle lead to consider a simpler system, which stability implies the stability of original one. An application to Hopfield's neural networks illustrates the work.

Robust stabilization of large-scale systems with nonlinear uncertainties via decentralized state feedback

The present paper is concerned with the decentralized stabilization problem for a class of large-scale systems with time-varying interconnected matrices and nonlinear uncertainties. A new sufficient condition is proposed for asymptotically stabilizing the large-scale perturbed systems with a prescribed stability degree by using decentralized state-feedback controllers. All the information needed here is only the possible bounds of the time-varying interconnected matrices and nonlinear uncertainties. This condition is shown to be less conservative than the ones reported recently. The results can be extended to a class of large-scale systems with delays. Two illustrative examples are included to demonstrate the superiority of the obtained results.

大規模システムの分散安定化

大規模システムの分散安定化

Comment regarding "On delay-independant stability of large-scale systems with time delays"

This paper comments the result of a recent paper by Xu (ibid., vol.40, p.930-3 (1995)). The commenter points out that these results have already been published in a more general framework by him (Int. J. Contr., vol.45, no.6 (1987)), and the following points are also clarified: the state which has to be considered and a connection with the passivity theorem.

Stability of large scale systems and the method of cone-valued lyapunov functions

Stability of large scale systems and the method of cone-valued lyapunov functions

On delay-independent stability of large-scale systems with time delays

A new criterion for delay-independent stability of linear large scale time-delay systems is deduced by employing an improved Razumikhin-type theorem and the m-matrix properties. An illustrative example is given to demonstrate the superiority of the obtained results to those in the literature.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability analysis of large-scale systems with delays

New sufficient conditions for delay-independent asymptotic stability of large-scale systems are presented by using the properties of matrix norm and measure. The proposed method is simple and effective.

On exponential stability of large scale systems with unbounded delay

In this paper, we first give a sufficient and necessary condition to guarantee the exponential stability of a special system with unbounded delay, then by using the delay-differential comparison theorem, obtain some simple criteria for the exponential stability of large scale systems with unbounded delay.

Robust stability of large-scale systems which contain time-invariant lur'e-type uncertainties in subsystems and norm-bounded uncertainties in interconnections

In this paper a new frequency-domain condition for the robust stability of a class of large-scale systems is derived. It is assumed that each subsystem contains one time-invariant nonlinearity satisfying a sector condition, and that the interconnecting functions are linearly bounded by the norms of the scalar outputs of subsystems. In deriving the above such Lur'e-type Lyapunov functions of subsystems are constructed so that their weighted sum is a Lyapunov function of the overall system. This condition is potential to give a sharper result than the circle-condition-type result which was obtained previously. Furthermore, a method to estimate the domain of attraction using the above Lyapunov function is also given when the sector condition is satisfied only locally.

Practical Stability of Large Scale Dynamic Systems with Impulsive Solutions

Practical stability of large scale dynamic systems with impulsive solutions which has not yet been studied up to now is presented and taken into account. Using comparison principle between two different dimensional systems, scale and vector Lyapunov functions and impulsive differential inequalities, we obtained sufficient conditions in a unified way for various practical stability of large scale system (1) which is decomposed into l subsystems of forms (2 i ), (3 i ) or (4 i ). The basic idea is, the practical stability properties of a scalar equation or a lower dimensional system with impulsive solutions imply the corresponding practical stability properties of the large scale system (1) with impulsive solutions.

Decentralized stabilization of large-scale systems with structured uncertainties

Abstract The decentralized stabilization problem of large-scale systems with structured time-varying uncertainties is considered. A new sufficient condition is established for asymptotically stabilizing the large-scale perturbed systems using decentralized state feedback controllers. We also consider the use of optimal Perron weightings to reduce conservatism and the extension of the results to discrete-time large-scale systems with structured uncertainties. An illustrative example is given to demonstrate that the new sufficient condition is less conservative than the one reported recently. Another example is also given to illustrate the use of the sufficient condition for stability robustness of discrete-time large-scale systems.

A constructive procedure for stabilization of large-scale systems by informationally decentralized controllers

A constructive procedure for the design of an informationally decentralized stabilization scheme for large-scale interconnected systems is presented. The design procedure is based on a stability result that uses the notion of block-diagonal dominance in matrices and considerably improves on the existing results in either enlarging the class of interconnections for which the design of a stabilization scheme can be satisfactorily conducted or yielding lower values of controller gains for a given interconnection pattern. It is demonstrated how the controller gains can be tailored systematically to the existing interconnection pattern within the overall system. >

ON DECENTRALIZED OBSERVATION AND DECENTRALIZED CONTROL OF LARGE SCALE SYSTEMS

In this paper, the problem of decentralized observation and decentralized control of linear, time-invariant large scale systems is studied. Based on conventional observer theory, the necessary and sufficient conditions for existence of completely decentralized observer are obtained. Moreover, the necessary and sufficient condition is given for stabilization of large scale systems by local output with state of the subsystem estimated through the completely decentralized observer.

Stability of large-scale systems with weakly interacting subsystems

Stability of large-scale systems with weakly interacting subsystems

Successive overrelaxation iteration for the stability of large scale systems

The successive overrelaxation iteration is used to investigate the stability of large scale systems, and some sufficient conditions such that the zero solution of an overall system is asymptotically stable are obtained, which only depend upon the fundamental matrices of the variational isolated subsystems and the interconnected matrices.