REALISASI MINIMAL DARI RESPONS IMPULS DISCRETE EVENT SYSTEMS LINEAR WAKTU INVARIAN MENGGUNAKAN ALJABAR MAX-PLUS

Consider an arbitrary linear time invariant discrete event system (DES). Theoretically, the input-output aquation of this DES can always be determined. In fact, it is often only known the impluse response, i.e. how the syste response an impulse given to it. Therefore, the system matrices A, B, and C need to be determined first. This is called realization for impulse response of the system. This system matrices then can be used to determine the input-output equation of considered DES. We will discuss about the realization existence condition for impulse response of linear time invariant DES and the algorithm to construct it. As teh results, it will be shown that the existence of realization depennds on the ultimately periodic property of the impulse reponse given. This is an analog property to the existence condition for realization over conventional algebra, which depend on the t-reccurent property. Furthermore, Hankel matrix holds a very important role on the process of finding realization. In the realization over ring and field, the rank of this matrix provides the minimal order of the system. For max-plus algebra, this rank only provides the bounds of minimal order for the system