On the Interval Stability of Weak-Nonlinear Control Systems with Aftereffect

Shatyrko, Andrey V.; Khusainov, D. Ya.

doi:10.1155/2016/6490826

Cited by 7 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We naturally encounter with the robust (or interval) stability concept when we study real‐life problems in control theory . A system is called robust (interval absolutely stable), if it is absolutely stable for each matrix, the elements of which lie in the specified intervals . This definition supports the method we propose in this paper.…”

Section: Introductionsupporting

confidence: 57%

“…Differential equations with interval coefficients arise also when stability problems are examined. We naturally encounter with the robust (or interval) stability concept when we study real‐life problems in control theory . A system is called robust (interval absolutely stable), if it is absolutely stable for each matrix, the elements of which lie in the specified intervals .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On differential equations with interval coefficients

Gasılov

Amrahov

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In this study, a new approach is developed to solve the initial value problem for interval linear differential equations. In the considered problem, the coefficients and the initial values are constant intervals. In the developed approach, there is no need to define a derivative for interval-valued functions. All derivatives used in the approach are classical derivatives of real functions. The reason for this is that the solution of the problem is defined as a bunch of real functions. Such a solution concept is compatible also with the robust stability concept.Sufficient conditions are provided for the solution to be expressed analytically. In addition, on a numerical example, the solution obtained by the proposed approach is compared with the solution obtained by the generalized Hukuhara differentiability. It is shown that the proposed approach gives a new type of solution. The main advantage of the proposed approach is that the solution to the considered interval initial value problem exists and is unique, as in the real case. KEYWORDSbunch of functions, interval differential equations, linear differential equations MSC CLASSIFICATION34A12; 65L05; 03E75; 68W25

show abstract

Section: Introductionsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

On differential equations with interval coefficients

Gasılov

Amrahov

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…However, time delays cannot always be avoided in practice and they often cause the system's instability and poor performance. Recently, many researchers have studied many kinds of dynamic systems with time delays (see [3,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]). Thus, some researchers naturally have devoted efforts to investigating the corresponding state bounding estimation for the dynamic systems with time delays.…”

Section: Introductionmentioning

confidence: 99%

State bounding estimation for a linear continuous-time singular system with time-varying delay

Xiao

2019

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

“…Since the pioneering work in the last century by Lurie [1,2], much related research has been carried out [3][4][5][6][7]. For instance, [8] studied the indirect regulation on a nonlinear system with delay argument; [9] investigated the stabilization on a nonlinear system with time delay.…”

Section: Introductionmentioning

confidence: 99%