LMIs, interior point methods, complexity theory, and robustness analysis

Let /spl delta//sub /spl Sigma// be a measure of the relative stability of a stable dynamical system /spl Sigma/. Let /spl tau//sub A(/spl Sigma//) be a measure of the computational efficiency of a particular algorithm A which verifies the stability property of /spl Sigma/. For two representative ca...

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Bibliographic Details
Main Authors: Mesbahi, M., Papavassilopoulos, G.P.
Format: Conference Proceeding
Language:English
Subjects:
Algorithm design and analysis
Complexity theory
Computational efficiency
Control systems
Particle measurements
Q measurement
Robust control
Robust stability
Robustness
Stability analysis
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Summary:Let /spl delta//sub /spl Sigma// be a measure of the relative stability of a stable dynamical system /spl Sigma/. Let /spl tau//sub A(/spl Sigma//) be a measure of the computational efficiency of a particular algorithm A which verifies the stability property of /spl Sigma/. For two representative cases of /spl Sigma/, we demonstrate the existence of a particular measure /spl delta//sub /spl Sigma// and an algorithm A such that, /spl delta//sub /spl Sigma///spl tau//sub A(/spl Sigma//)=c where c depends possibly on the dimension of the system /spl Sigma/ and parameters which are specific to the algorithm A, but independent of any other system characteristics. In particular, given /spl Sigma/ and A, one can estimate /spl delta//spl Sigma/ by measuring /spl tau//sub A(/spl Sigma//).
ISSN:0191-2216
DOI:10.1109/CDC.1996.577603