scholarly journals Stabilization of time-delay systems through linear differential equations using a descriptor representation

2009 ◽  
Author(s):  
Alexandre Seuret ◽  
Karl H. Johansson
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Linear Differential

scholarly journals Existence and Stability Results on Hadamard Type Fractional Time-Delay Semilinear Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1242
Author(s):  
Nazim Mahmudov ◽  
Areen Al-Khateeb
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Explicit Form ◽  
Nonlinear Equations ◽  
Matrix Function ◽  
Linear Differential Equations ◽  
Existence And Stability ◽  
Linear Differential ◽  
Stability Results

A delayed perturbation of the Mittag-Leffler type matrix function with logarithm is proposed. This combines the classic Mittag–Leffler type matrix function with a logarithm and delayed Mittag–Leffler type matrix function. With the help of this introduced delayed perturbation of the Mittag–Leffler type matrix function with a logarithm, we provide an explicit form for solutions to non-homogeneous Hadamard-type fractional time-delay linear differential equations. We also examine the existence, uniqueness, and Ulam–Hyers stability of Hadamard-type fractional time-delay nonlinear equations.

scholarly journals Fast Generation of Stability Charts for Time-Delay Systems Using Continuation of Characteristic Roots

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Surya Samukham ◽  
Thomas K. Uchida ◽  
C. P. Vyasarayani
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Grid Point ◽  
Galerkin Approximation ◽  
Computational Effort ◽  
Numerical Continuation ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Characteristic Roots ◽  
The Stability

Abstract Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging because DDEs are infinite-dimensional. We propose a new approach to quickly generate stability charts for DDEs using continuation of characteristic roots (CCR). In our CCR method, the roots of the characteristic equation of a DDE are written as implicit functions of the parameters of interest, and the continuation equations are derived in the form of ordinary differential equations (ODEs). Numerical continuation is then employed to determine the characteristic roots at all points in a parametric space; the stability of the original DDE can then be easily determined. A key advantage of the proposed method is that a system of linearly independent ODEs is solved rather than the typical strategy of solving a large eigenvalue problem at each grid point in the domain. Thus, the CCR method can significantly reduce the computational effort required to determine the stability of DDEs. As we demonstrate with several examples, the CCR method generates highly accurate stability charts, and does so up to 10 times faster than the Galerkin approximation method.

Learning Control for Time-Delay Systems with Multi-Tasks

1995 ◽  
Vol 115 (1) ◽  
pp. 167-168
Author(s):  
Tohru Takahashi ◽  
Yoshirou Tajima ◽  
Kohji Shirane ◽  
Naoki Matsumoto
Keyword(s):  
Time Delay ◽  
Learning Control ◽  
Delay Systems ◽  
Time Delay Systems
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