A Meaning of the Decoupling by Feedback of Linear Functional Time Systems

More Results on Decomposition and Decoupling of Single Relation Systems

“…Results in Saito and Mesarovic (1985) and Saito (1988) show that this is a very effective concept to study the problem about whole and parts. Examples in Saito and Mesarovic (1985) and Mesarovic and Takahara (1975) were given to show the close relation between the research of the general systems theory, based on set theory, and the research of linear systems of ordinary differential equations. This gives us a wide and important space to do research.…”

“…The concept of general feedback systems was studied intensively by Mesarovic and Takahara (1975). Saito and Mesarovic (1985) introduced and studied the concept of linear feedback systems and gave a remarkable example to show Downloaded by [Nanyang Technological University] at 19:11 10 June 2016 the relation between general systems theory and the linear systems theory of ordinary differential equations. Here, we use the definition of feedback systems given by Saito (1988).…”

“…We say that the system S can be decoupled by feedback (Saito and Mesarovic 1985), provided that there exists a linear system Sf C Y x X such that…”

“…His work reflects one of the basic viewpoints of modeling of the systems theory and includes the decomposition theory of a finite automaton as a special case. Saito and Mesarovic (1985), Mesarovic and Takahara (1975), and Saito (1988) introduced the concept: of decoupling by feedback. One of the goals of introducing the concept is to see when and how a given system can be decomposed into a non-interacted system by a feedback transformation, which has a structure easier for us to the set S is called an input-output system (Mesarovic and Takahara 1975), and the sets X and Yare called the input space and the output space of the system S. The system S is termed as a functional system (Mesarovic and Takahara 1975), provided that S is a function from the input space X into the output space Y.…”

“…When the linear system S, in addition, is functional, the system S is called a functional linear system. For a general linear system S, the null space (Saito and Mesarovic 1985) of the system S, denoted by N(S), is defined by NISI = (X r X: I r O l r S) (1)…”