Optimal Solutions for Non-consistent Singular Linear Systems of Fractional Nabla Difference Equations
Optimal Solutions for Non-consistent Singular Linear Systems of Fractional Nabla Difference Equations
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DOI：
10.1007/s00034-014-9930-2
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
I. Dassios
中科院分区：
文献类型：
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作者：
I. Dassios
本文研究了一类系数为常数矩阵的非相容奇异线性分数阶nabla差分方程组的最优解。我们考虑了矩阵是正方形且首项系数奇异、非正方形以及正方形且矩阵束的行列式恒为零的情况。然后，我们首先研究了给定非一致初始条件的系统，并给出了最优解。此外，我们考虑了系统的边界条件，并提供了两种情况下，当边值问题是不一致的，当它有无穷多个解决方案的最优解。最后，研究了分数阶Nabla差分方程奇异非齐次线性控制系统的Kalman滤波器。数值例子证明了我们的理论。
In this article, we study optimal solutions for a class of non-consistent singular linear systems of fractional nabla difference equations whose coefficients are constant matrices. We take into consideration the cases that the matrices are square with the leading coefficient singular, non-square and square with a matrix pencil which has an identically zero determinant. Then, first we study the system with given non-consistent initial conditions and provide optimal solutions. Furthermore, we consider the system with boundary conditions and provide optimal solutions for two cases, when the boundary value problem is non-consistent and when it has infinite solutions. Finally, we study the Kalman filter for singular non-homogeneous linear control systems of fractional nabla difference equations. Numerical examples are given to justify our theory.