Dr.B.V.APPA RAO, Dept of Maths has authored a paper and was published in International Journal of Advances in Engineering, Science and Technology (IJAEST)

This paper presents several fundamental results concerning the controllability and observability criteria for ?-differential matrix Sylvester system

X?(t) = A(t) X(t) + X(t) B(t) + F1(t) U(t) F2

*(t), X(t0) = X0, with output signal

Y(t)= K1(t)X(t)K2

*(t) and control U(t). First, we convert the system into a corresponding Kronecker product system with the help of Kronecker product technique, and its general solution is presented in terms of two transition matrices of the systems X?(t) = A(t)X(t) and X?(t) = B*(t)X(t). Then, a set of necessary and sufficient conditions are presented for the complete controllability and complete observability of the ?-differential Kronecker product system. 2000 Mathematics subject classification. 93B05, 93B07, 49K15.

Key words and phrases: Transition matrices, timescale, Kronecker product, controllability and observability.