Study of Control Theory Construction Based on Computer Algebra

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The aim of this study is to construct the new control system theory based on the computer algebra. In 1990, the main work was to research the 2-D system theory and the following results were obtained.1) Coprimeness of 2-D transferfunction and stability of 2-D system : The coprimeness is quite difference from the one of 1-D transferfunction. Then the concepts such as zero-coprimeness and factor coprimeness should be considered. In addition, minor coprimeness was necessary in the case of 2-d transferfunction matrix. Here the new concept - OMEGA -coprimeness was defined and consequently both coprimeness and stability condition for 2-D system could be discussed uniformly.2) Synthesis algorithms of stabilizable compensator for 2-D system : The algorithm is reduced to solving the bilateral matrix equation AX+BY=C. In this work the software package for the matrix equation has been developed based on REDUCE and it was clarified that there existed the deep relationship between the 2-D system and the computer algebra.In 1991, based on the above results, 2-D system theories were extended to the general n-D system theories and following results were obtained.3) Stability of n-D system : Recently the new stability concept for n-D system, -practical stability- was introduced. Here the synthesis algorithms of the practical stabilizable compensator were established. And the Computer Aided Design system was also developed.4) Dynamical simulation of n-D system : The dynamical response of n-D ststem is very complex. Then the user friendly simulator for n-D system was developed by using computer graphics and REDUCE.