Results 1 to 10 of about 68 (58)
Journal of Mathematical Analysis and Applications, 1987 The author studies the poinwise completeness and degeneracy for functional differential equations of the type \[ x'(t)=A_ 0x(t)+\sum^{m}_{i=1}A_ ix(t-h_ i)+\int^{0}_{- h}B(s)x(t+s)ds+f(t), \] \(t\geq 0\); \(x(0)=g^ 0\); \(x(s)=g(s ...
Shin-Ichi Nakagiri
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Pointwise degeneracy of linear, time-invariant, delay-differential equations
Journal of Differential Equations, 1972 openaire +3 more sources
Bulletin of the Polish Academy of Sciences Technical Sciences, 2020 Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems are established. It is shown that if the fractional system is pointwise complete in one step (q = 1), then it is also pointwise complete for q = 2, 3…
Tadeusz Kaczorek, Ł. Sajewski
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International Journal of Applied Mathematics and Computer Science, 2020 The Drazin inverse of matrices is applied to the analysis of pointwise completeness and pointwise degeneracy of fractional descriptor linear continuous-time systems. It is shown that (i) descriptor linear continuous-time systems are pointwise complete if and only if the initial and final states belong to the same subspace, and (ii) fractional ...
Tadeusz Kaczorek, Andrzej Ruszewski
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International Journal of Applied Mathematics and Computer Science, 2020 The subject is continuous time linear systems for vector functions \(x(t)\) containing fractional derivatives \((d^\alpha /dt^\alpha) x(t)\). The derivative is the \textit{Caputo fractional derivative} \[ \frac{d^\alpha}{dt^\alpha} x(t) = \frac{1}{\Gamma(n - \alpha)} \int_0^t \frac{1}{(t - \tau)^{\alpha - n + 1}} \frac{d^n}{d\tau^n} x(\tau) d\tau \quad
Kaczorek Tadeusz, Sajewski Łukasz
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Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils [PDF]
International Journal of Applied Mathematics and Computer Science, 2015 Abstract Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
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Journal of Automation, Electronics and Electrical Engineering, 2023 The Drazin inverse of matrices is applied to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor standard and fractional linear continuous-time and discrete-time systems. It is shown that: 1) The descriptor linear continuous-time system is pointwise complete if and only if the initial and final states belong to the ...
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Bulletin of the Polish Academy of Sciences Technical Sciences, 2019 The Drazin inverse of matrices is applied to analysis of the pointwise completeness and of the pointwise degeneracy of the fractional descriptor linear discrete-time systems. Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of the fractional descriptor linear discrete-time systems are established.
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Bulletin of the Polish Academy of Sciences Technical Sciences, 2015 Abstract Pointwise completeness and pointwise degeneracy of the fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for the pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
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