Calculation of the structured singular value with a reduced number of optimization variables

• Published in: IEEE transactions on automatic control Vol. 37; no. 10; pp. 1612 - 1616
• Main Authors: Latchman, H.A., Norris, R.J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.1992; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Laboratories; Matrix converters; MIMO; Optimal control; Optimization methods; Robustness; Transfer functions; Uncertainty; Upper bound; Matrix calculus; Uncertain system; Optimization; Vector optimization
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/9.256396

For the case of an n*n uncertainty matrix with n/sup 2/ nonzero 1*1 blocks, the structured singular value technique with similarity scaling suffers from the disadvantage of having to expand an n*n matrix problem to an n/sup 2/*n/sup 2/ matrix optimization problem with n/sup 2/-1 free variables. It is shown that for elementwise, magnitude-bounded uncertainties, the structure of the problem may be exploited to yield a similarity scaling method which uses no more than 2(n-1) rather than n/sup 2/-1 independent optimization parameters. A simple extension of this result shows that a reduction in the number of independent optimization variables is also possible for more general block-structured uncertainties. A more efficient implementation of the vector optimization method developed by M.K.H. Fan and A.L. Tits (1986) is also proposed. Several examples are included to illustrate the results.< >