KETERKENDALIAN SISTEM LINIER DIFERENSIAL BIASA TIME-VARYING DAN SISTEM LINIER DIFERENSIAL PARSIAL DENGAN PENDEKATAN MODUL ATAS OPERATOR DIFERENSIAL

Abstract

Suppose,,,,] 1 2 3 [n D  K d d d d d d linear differential operators with coefficients in K, which meet  a K; he = adi + ia. D is a linear differential carrier ring with intermediate properties else: D does not contain a zero divide, is not commutative, and for every d d D i j, , i, j  1, , n and for every a, b  K apply i j i j i j ad (bd)  abd d  a ( b) d. Let M be a top module D formed from an ordinary differential linear system (OD) time-varying or partial differential linear (PD) systems under control. The relationship between systems OD or linear PD with module M over D is a linear OD or PD system if and only if M the top module D determined by the equation is a torque-free module. Therefore to indicate a system of OD or PD linear simply indicated module formed by the equation is torque-free, expressed in a formal test to indicate a module over D is torque free. and if it is associated with a plane linear differential operators are controlled linear PD control systems if and only if parametrizable.