CONTROLLABILITY AND OBSERVABILITY OF MATRIX SYLVESTER SYSTEMS ON TIMESCALES

This paper presents several fundamental results concerning the controllability and observability criteria for Δdifferential matrix Sylvester system X Δ (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 Δ (t) = A(t)X(t) and X Δ (t) = B * (t)X(t). Then, a set of necessary and sufficient conditions are presented for the complete controllability and complete observability of the Δ-differential Kronecker product system. 2000 Mathematics subject classification. 93B05, 93B07, 49K15.