Generalized Nyquist Tests for Robust Stability: Frequency Domain Generalizations of Kharitonov’s Theorem

Description And Analysis Of Interval Systems

“…Substantially simpler geometric proofs can be found e.g. in (Anagnost et al 1989;Dasgupta 1988;Minnichelli et al 1989) or in (Matušů and Prokop 2008). Besides, an array of improvements of the Kharitonov theorem can be found in literature.…”

Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems

“…In this regard, mention can be made of [11], [12], [13], where frequency-like methods are applied to the characteristic (pseudo) polynomial of a fractional-order system, of [14], where reference is made to systems in Lure's form, of [15], where non-commensurate delay systems are considered, and of [16], [17] that present adaptations of the classical algebraic criteria of Routh and Jury. Quite understandably, these contributions naturally pertain to the broader, and by now well-established, line of research on root clustering [18], [19], [20], robust and D-stability [21], [22], [23]. Most of the aforementioned results require a fairly strong mathematical background and lead to tests that are not easily implemented.…”

Robuste Regelung

“…In del' Zwischenzeit wurde in[21] ein einfacherer Beweis angegeben, del' auf dem Prinzip des Nullausschlusses aus der Wertemenge von p(jw, a) basiert, d.h. der Ursprung darf nicht in der Wertemenge enthalten sein. In del' Zwischenzeit wurde in[21] ein einfacherer Beweis angegeben, del' auf dem Prinzip des Nullausschlusses aus der Wertemenge von p(jw, a) basiert, d.h. der Ursprung darf nicht in der Wertemenge enthalten sein.…”