HIGH-INDEX DIFFERENTIAL-ALGEBRAIC EQUATIONS

In the last few years there has been considerable research on differential algebraic equations (DAEs) f(x', x, t) = 0, where f(x') is identically singular. The index provides one measure of the singularity of a DAE. Most of the numerical analysis literature on DAEs to date has dealt with DAEs with indices no larger than three, because of technical difficulties and because many basic applications including constrained mechanical systems have this index. This paper discusses several situations where DAEs of index higher than three occur naturally. It will also discuss the relationship between certain concepts in nonlinear control theory such as relative degree and zero dynamics, the index, and constrained mechanical systems.