On parametric asymptotic stability of large-scale systems

Martynyuk, À. À.; Khoroshun, À. S.

doi:10.1007/s10778-008-0069-3

Cited by 12 publications

(4 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is reasonable to analyze the behavior of uncertain systems [10,13] on a time scale in the way proposed here and to obtain results for a time scale as in [11].…”

Section: Definitionmentioning

confidence: 99%

Sufficient conditions of connective stability of motion on time scale

Luk'yanova

Martynyuk

2013

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

Introduction. The concept of connective stability was introduced in [14] in studying the motion of large-scale systems. This type of stability for various types of systems of equations is addressed in many studies. For example, continuous-time systems are studied in [9,15,16] and discrete-time systems in [2,6]. The theory of dynamic systems on a time scale [5] allows simultaneous description of the dynamics of both continuous-and discrete-time systems. Nowadays, such systems are the subject of numerous studies (see [1,3,12] and the references therein).The present paper is a continuation of the study [1]. We will use the principle of comparison with a vector Lyapunov function and establish the sufficient conditions of the connective stability of motion on a time scale. Basic Notation and Definitions.A time scale T is an arbitrary nonempty closed subset of the real numbers R. The basic concepts and theorems of time-scale calculus such as the definitions of derivative and integral, differentiation and integration rules, definitions of regressive and rd-continuous functions, definitions of regressive and rd-continuous matrices are detailed in [1,5]. Some necessary concepts and definitions are given below.A function f

show abstract

“…It is reasonable to analyze the behavior of uncertain systems [10,13] on a time scale in the way proposed here and to obtain results for a time scale as in [11].…”

Section: Definitionmentioning

confidence: 99%

Sufficient conditions of connective stability of motion on time scale

Luk'yanova

Martynyuk

2013

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…This solution describes the quasiperiodic motion of a system with two degrees of freedom. The present paper establishes uniform asymptotic stability conditions [8] for one class of nonlinear quasiperiodic systems. For the linear approximation of this system, we will set up a Lyapunov function [3,6] by decomposing the original system and employing the ideas behind the method of matrix Lyapunov functions [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Setting up Lyapunov functions for the class of systems with quasiperiodic coefficients

Lila

Martynyuk

2008

Int Appl Mech

View full text Add to dashboard Cite

The paper proposes a method to set up a matrix-valued Lyapunov function for a system of differential equations with quasiperiodic coefficients. This function is used to establish asymptotic stability conditions for a class of linear systems Keywords: Lyapunov matrix-valued function, differential equations with quasiperiodic coefficients, asymptotic stability conditions 1. Introduction. Quasiperiodic motion [7] occurs in an elementary linear conservative system [9] with two degrees of freedom. Its solution has the form

show abstract

“…We will use the concept of parametric stability introduced in [7] and developed in [3,5,9,11] to study the stability properties of one class of systems of the form (1) dependent on some parameters [13]. Unlike the standard approach, we will assume that the equilibrium state is not fixed at the origin of coordinates, its position depending on the values of the parameters.…”

mentioning

confidence: 99%