THE STRUCTURE OF TRUNCATED LAURENT SERIES SPACE THAT ASSOCIATED WITH THE BEHAVIOR OF A LINEAR SYSTEM AROUND THE INFINITE POLE - RACHMAPUTRI (NIM: 30110010), GANTINA
In this dissertation, we shall study the structure of truncated Laurent seriesspace that associated with a behavior of a linear system around the in_nitepole. The truncated Laurent series module over a formal series ring have animportant role as a state space of a linear system around the in_nite pole.Meanwhile, the truncated Laurent series module over a polynomial ring havebeen used as a state space of a linear system in the behavioral framework.Fuhrmann studied that the behavioral framework of a linear system can beexplored through the structure of the truncated Laurent series module over apolynomial ring. This study can be done based on the fact that there is a one-to-one correspondence between the collection of behaviors and the collection ofsubmodules of the truncated Laurent series module over a polynomial ring. Inthis dissertation, we have obtain the equivalent correspondence in the context of the truncated Laurent series module over a formal series ring. This one-to-one correspondence obtained through a construction of a bilinear on thetruncated Laurent series space.We also study the complete notion of a subspace of a formal series space in theterms of an algebraic condition connected to a certain projection that intro-duced by Fuhrmann and adapted it to obtain the characterization of closed submodules of a _nite rank free module over a complete discrete valuationdomain. This study deduced by identifying and adapting notions, properties andapproaches which are used by Fuhrmann.Keywords: behavior, bilinear, discrete valuation domain, dynamical system, linear system, truncated Laurent series space.