Structural decomposition of linear multivariable systems using symbolic computations

Abstract

We introduce a procedure written in the mathematics software suite Maple, which transforms linear time-invariant systems to a special coordinate basis that reveals the internal structure of the system. The procedure creates exact decompositions, based on matrices that contain elements represented by symbolic variables or exact fractions. Throughout the procedure, transformations are constructed with the goal of avoiding unnecessary changes to the original states. The procedure is intended to complement numerical software algorithms developed by others for the same purpose. We discuss various system-theoretic aspects of the special coordinate basis as well as numerical issues related to the decomposition procedure, and illustrate use of the procedure by examples.

Keywords:

• linear systems theory
• symbolic computations
• finite zeros
• infinite zeros
• invertibility
• geometry theory

Acknowledgements

The work of Håvard Fjær Grip is supported by the Research Council of Norway. The work of Ali Saberi is partially supported by National Science Foundation grant NSF-0901137 and NAVY grants ONR KKK777SB001 and ONR KKK760SB0012.