In this talk, 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.
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