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On several variable zero sets and application to MIMO robust feedback stabilization

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3 Author(s)

Given a complex-valued function f which depends on m real variables s_1,\cdots ,s_m and n complex parameters A_1,\cdots ,A_n , we describe a method of finding the zero set V of all zeros of f in some given set G in R^m when each parameter A_i is allowed to vary in some given set K_i in the extended complex plane \overline {\bf C} = {\bf C} cup{\infty } . This mathematical tool is applied in the paper to determine the complete space of output (or state) feedback gains, which allows robust stabilization of a linear MIMO system under uncertainty conditions. The system may be continuous or discrete. Also, the stabilization may be "relative," i.e., with safety margins. Design examples are provided.

Published in:

IEEE Transactions on Circuits and Systems  (Volume:34 ,  Issue: 10 )