Conditions of asymptotic stability for linear homogeneous switched systems

Ivanov, G. G.; Alferov, Gennady; Sharlay, Artem; Efimova, Polina

doi:10.1063/1.4992263

Cited by 25 publications

(13 citation statements)

References 24 publications

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“…Repeating the proof of Theorem 12 [31], it is easy to show that there exist derived numbers for which the following relation holds:…”

Section: Stability Of Almost Periodic Solutionsmentioning

confidence: 93%

“…This derivative exists and is finite by convexity of ψ(ω n , x). It follows from Theorem 12 [31] that there exist two sequences {ζ 1 (ω n )} and {ζ 2 (ω n )} such that…”

Section: Theorem 9 If Equationmentioning

confidence: 99%

“…Over the last years, the question of studying almost periodic functions in robotics [15][16][17][18][19][20][21], dynamic systems [22][23][24][25][26], stability theory [27][28][29][30][31], control systems for space objects [32][33][34], and economy problems [35][36][37][38] arose significantly.…”

Section: Introductionmentioning

confidence: 99%

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Almost Periodic Solutions of First-Order Ordinary Differential Equations

et al. 2018

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Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In the works of Lebedeva [1], regarding the number of periodic solutions of equations first order, they required a high degree of smoothness. Franco et al. required the smoothness of the second derivative of the Schwartz equation [2]. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty.

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“…Repeating the proof of Theorem 12 [31], it is easy to show that there exist derived numbers for which the following relation holds:…”

Section: Stability Of Almost Periodic Solutionsmentioning

confidence: 93%

“…This derivative exists and is finite by convexity of ψ(ω n , x). It follows from Theorem 12 [31] that there exist two sequences {ζ 1 (ω n )} and {ζ 2 (ω n )} such that…”

Section: Theorem 9 If Equationmentioning

confidence: 99%

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Almost Periodic Solutions of First-Order Ordinary Differential Equations

et al. 2018

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“…Periodic solutions take an important part in the qualitative theory of differential equations and in applied problems [3]. The analysis problems for periodic solutions of differential equations arise in classical mechanics, celestial mechanics [4][5][6][7][8][9][10][11][12][13][14][15], space robotics [16][17][18][19][20][21][22][23][24], in modeling of economic processes [25][26][27][28][29]. However, there is no general approach to study periodic solutions of differential equations.…”

Section: Introductionmentioning

confidence: 99%

A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

et al. 2019

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In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

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“…As for the dynamic analysis [3] of the functioning of a bilaterally controlled model of a space robot from the control arm, it has already been carried out [4] and its results, including the conditions for achieving stability of the control, are given in [8][9][10][15][16][17][18]. This article presents a dynamic analysis of the process of functioning of the local control system of the space robot while tracking the program trajectories formed in the process of training at the ground control center.…”

mentioning

confidence: 99%

A New Method for a Remote Control of a Robotic Manipulator

Kadry¹,

Alferov

Korolev

et al. 2021

Int. J. Onl. Eng.

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A new method of remote control of a space robot designed to perform operations in a complex external environment with objects that can move freely in space or are limited by holonomic bonds that limit their possible movements is proposed. This is typical when performing Assembly operations in space exploration. The method is based on the use of an important feature that characterizes each operation performed. This is a passport of the operations performed on the interaction of the working tool of the robot with objects in the external environment

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Conditions of asymptotic stability for linear homogeneous switched systems

Cited by 25 publications

References 24 publications

Almost Periodic Solutions of First-Order Ordinary Differential Equations

Almost Periodic Solutions of First-Order Ordinary Differential Equations

A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

A New Method for a Remote Control of a Robotic Manipulator

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