N-dimensional stability margins computation and a variable transformation

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.