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In this talk, we will present a report on the progress of development of a Mathematica-based package for design and an analysis of large-scale control systems in standard state-space forms. The report is based on the work performed by me at Wolfram Research, during the summer of 2005 under the direction of Dr. Igor Bakshee of Wolfram Research and scientific advising of Professor Biswa Nath Datta of Northern Illinois University.
It is to be noted that though there are excellent numerical methods currently available for linear control systems design and analysis for dense problems (see the recent book [1]), algorithms for large and sparse problems are rare. On the other hand, there are practical situations, such as the design of large space structures, power systems, computer networks, and so on, that give rise to very large and sparse control problems. In the last few years, only a few algorithms have been developed for large-scale solutions of some of the important linear algebra problems associated with control systems design and analysis, including Sylvester, Lyapunov, and Riccati equations; partial pole placement; and model reduction (see [1], [2]). Some of these algorithms have been implemented in my work at Wolfram Research, and work on the others is in progress. The intended package is an extension of the existing Wolfram Research packages, Control System Professional, by Igor Bakshee [3]) and Advanced Numerical Methods, by Biswa Nath Datta and Daniil Sarkissian [4]. At present, there does not exist any control software package for large-scale control systems. When completed, the present package will be the first of its kind.
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