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N-dimensional stability margins computation and a variable transformation

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2 Author(s)
Walach, E. ; Technion-Israel Institute of Technology, Haifa, Israel ; Zeheb, E.

Stability margins for N-dimensional ( N \geq 2 ) linear discrete causal systems are defined, following a definition suggested recently in the literature for N = 2. These can serve as a measure, in some sense, for the tendency of a stable N-D system to become unstable. Also presented is a new procedure for the computation of these stability margins, which is explicitly formulated. The computational complexity is equivalent to that of solving for one indeterminate a set of N + 1 real equations in N + 1 real indeterminates. Also, an N-dimensional expansion of a known variable transformation which preserves the core condition of stability is presented and used to considerably simplify N-dimensional stability tests and stability margins computations for a class of special cases. Numerical examples are also provided.

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:30 ,  Issue: 6 )