Name
Abstract | ||
|---|---|---|
A limiting property of the matrix exponential is proven: if the (1,1)-block of a 2-by-2 block matrix becomes “arbitrarily small” in a limiting process, the matrix exponential of that matrix tends to zero in the (1,1)-, (1,2)-, and (2,1)-blocks. The limiting process is such that either the log norm of the (1,1)-block goes to negative infinity, or, for a certain polynomial dependency, the matrix associated with the largest power of the variable that tends to infinity is stable. The limiting property is useful for simplification of dynamic systems that exhibit modes with sufficiently different time scales. The obtained limit then implies the decoupling of the corresponding dynamics. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/TAC.2013.2287112 | Automatic Control, IEEE Transactions |
Keywords | Field | DocType |
matrix algebra,polynomials,2-by-2 block matrix,dynamic system,limiting property,logarithmic norm,matrix exponential,negative infinity,polynomial dependency,time-scale separation,Limiting property,logarithmic norm,matrix exponential,time-scale separation | Skew-symmetric matrix,Nonnegative matrix,Mathematical analysis,Matrix function,Symmetric matrix,Hamiltonian matrix,Logarithm of a matrix,Matrix exponential,Block matrix,Mathematics | Journal |
Volume | Issue | ISSN |
59 | 4 | 0018-9286 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sebastian Trimpe | 1 | 19 | 9.14 |
| Raffaello D'andrea | 2 | 1592 | 162.96 |