Abstract
The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4) operations on average, which is an improvement over previous methods which have complexity O(n6), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.
Original language | English (US) |
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Pages (from-to) | 477-502 |
Number of pages | 26 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 28 |
Issue number | 2 |
DOIs | |
State | Published - 2006 |
Keywords
- Complex controllability radius
- Distance to uncontrollability
- Kronecker product
- Real eigen-value extraction
- Shift-and-invert Arnoldi
- Shifted inverse iteration
- Sylvester equation
- Trisection
ASJC Scopus subject areas
- Analysis