Stability crossing set for systems with two scalar-delay channels

Abstract This article studies the stability crossing set of linear time-invariant systems with two scalar-delay channels. This study is crucial to the complete stability analysis along the idea of D-subdivision. The characteristic quasipolynomial of such systems contains an exponential term with the sum of two delays (cross term) in its exponent. A complete parameterization and geometric characterization of the stability crossing set is conducted. It was found instrumental to relate it to an associated quasipolynomial without such a cross term.

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