Minkowski Geometric Algebra and the Stability of Characteristic Polynomials

摘要: A polynomial p is said to be Γ-stable if all its roots lie within a given domain Γ in the complex plane. The Γ-stability of an entire family polynomials, defined by selecting coefficients from specified sets, can verified (i) testing single member, and (ii) checking that “total value set” V * for along boundary ∂Γ does not contain 0 (V as set values each point on every possible choice coefficients). methods Minkowski geometric algebra —the sets plane — offer natural language stability analysis families polynomials. These are introduced, applied analyzing disk polynomials with selected circular disks In this context, may characterized union one-parameter disks, we show finite algorithm (a counterpart Kharitonov conditions rectangular coefficient sets) entails at most two real remain positive t, when curve γ(t).Furthermore, “robustness margin” determined computing polynomial.