▁can ▁be ▁carefully ▁put ▁into ▁a ▁super position ▁such ▁that ▁it ▁will ▁satisfy ▁the ▁second ▁equation . ▁This ▁is ▁one ▁common ▁method ▁of ▁approaching ▁boundary ▁value ▁problems . ▁ ▁Add itive ▁state ▁decomposition ▁ ▁Consider ▁a ▁simple ▁linear ▁system ▁: ▁ ▁By ▁super position ▁principle , ▁the ▁system ▁can ▁be ▁decom posed ▁into ▁▁▁▁ ▁with ▁ ▁Super position ▁principle ▁is ▁only ▁available ▁for ▁linear ▁systems . ▁However , ▁the ▁Add itive ▁state ▁decomposition ▁can ▁be ▁applied ▁not ▁only ▁to ▁linear ▁systems ▁but ▁also ▁non linear ▁systems . ▁Next , ▁consider ▁a ▁non linear ▁system ▁ ▁where ▁ ▁is ▁a ▁non linear ▁function . ▁By ▁the ▁add itive ▁state ▁decomposition , ▁the ▁system ▁can ▁be ▁‘ add it ively ’ ▁decom posed ▁into ▁▁▁▁ ▁with ▁ ▁This ▁decomposition ▁can ▁help ▁to ▁simplify ▁controller ▁design . ▁ ▁Other ▁example ▁applications ▁ ▁In ▁elect rical ▁engineering , ▁in ▁a ▁linear ▁circuit , ▁the ▁input ▁( an ▁applied ▁time - v ary ing ▁voltage ▁signal ) ▁is ▁related ▁to ▁the ▁output ▁( a ▁current ▁or ▁voltage ▁anywhere ▁in ▁the ▁circuit ) ▁by ▁a ▁linear ▁transformation . ▁Thus , ▁a ▁super position ▁( i . e ., ▁sum ) ▁of ▁input ▁signals ▁will ▁yield ▁the ▁super position ▁of ▁the ▁responses . ▁The ▁use ▁of ▁Fourier ▁analysis ▁on ▁this ▁basis ▁is ▁particularly ▁common . ▁For ▁another , ▁related ▁technique ▁in ▁circuit ▁analysis , ▁see ▁Super position ▁theorem . ▁ ▁In ▁physics , ▁Max well ' s ▁equations ▁imply ▁that ▁the ▁( poss ibly ▁time - v ary ing )