how can compute the (z1,z2) for
det [z1-A1 -A2; A3 z2-A4]=0?
in one dimensional we convert A to Jordan form, but for A2 & A3 against zero, you have mathematical approach for this problem?
Hi, if the different matrices have not a special structure (band, etc...) I think that a numerical resolution is possible only.
The idea is to relax the proposition by using S-procedure (as I do) or SOS (as some others do). The condition amount to testing the Hurwitz or Schur stability (it depends if the first dimension is continuous or discrete) of a transfer matrix (w.r.t. z2) over the imaginary axis or the unit circle (it depends if the second dimension is continuous or discrete). Thus, the idea is to prove the existence of a Lyapunov matrix which depends on a parameter describing either the imaginary axis or the unit circle. By invoking S-procedure, we derive a hierarchy of sufficient LMIs for structural stability. The hierarchy level is the degree of the Lyapunov matrix which is actually polynomial in some parameter. For a sufficiently large degree, the condition becomes necessary.
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