ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS

This note contains three main results. Firstly, a complete solution of theLinear Non-Homogeneous Matrix Differential Equations (LNHMDEs) is presented thattakes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input. Secondly, in order to characterise the dynamics of theLNHMDEs correctly,some important concepts such as the state, slow state (smooth state)and fast state (impulsive state) are generalized to the LNHMDE case and the solutionof the LNHMDEs is separated into the smooth (slow) response and the fast (implusive)response. As a third result, a new characterization of the impulsive free initial conditionsof the LNHMDEs is given.