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Stabilization of the inverted pendulum by fractional-order proportional-derivative (PD) feedback with two delays is investigated. This feedback law is obtained as a combination of PD feedback with two delays and fractional-order PD feedback with a single delay. Different types of stabilizability boundaries and the corresponding geometric and multiplicity conditions are determined using the D-subdivision method. The stabilizable region is depicted in the plane of the delay parameters for given fractional derivative orders. Several special cases and the concept of delay detuning are also discussed. It is shown that the admissible delay can be slightly increased compared to the integer-order PD feedback by introducing a fractional-order feedback term. [ABSTRACT FROM AUTHOR]

In this article we consider the γ‐stabilization of nth‐order linear time‐invariant dynamical systems using multiplicity‐induced‐dominancy‐based controller design in the presence of delays in the input or the output channels. A sufficient condition is given for the dominancy of a real root with multiplicity at least n+1 and at least n using an integral factorization of the corresponding characteristic function. A necessary condition for γ‐stabilizability is analyzed utilizing the property that the derivative of a γ‐stable quasipolynomial is also γ‐stable under certain conditions. Sufficient and necessary conditions are given for systems with real‐rooted open‐loop characteristic function: the delay intervals are determined where the conditions for dominancy and γ‐stabilizability are satisfied. The efficiency of the proposed controller design is shown in the case of a multilink inverted pendulum. [ABSTRACT FROM AUTHOR]

Single and double inverted pendulum systems subjected to delayed state feedback are analyzed in terms of stabilizability. The maximum (critical) delay that allows a stable closed-loop system is determined via the multiplicity-induced-dominancy property of the characteristic roots, that is the dominant (rightmost) roots are associated with higher multiplicity under certain conditions of the system parameters. Other methods such as tracking the changes of the D-curves with increasing delay and the Walton–Marshall method are also demonstrated for the example of the single pendulum. For the double inverted pendulum subjected to full state feedback, the number of control gains is four, and application of numerical methods requires therefore high computational effort (i.e. optimization in a four-dimensional space). It is shown that, with the multiplicity-induced-dominancy–based approach, the critical delay and the associated control gains can be determined directly using the characteristic equation and its derivatives. [ABSTRACT FROM AUTHOR]

The article relates an episode in the early-20th-century Hungarian press. The revue “Uj nemzedek” (“New Generation”) had an opinion column with Dezso Kosztolanyi (1885-1936) as its host. As a well-known writer and poet, Kosztolanyi tried to moderate the tone of the articles he published. One article received came from an influential journalist with powerful backings was very anti-Semitic and for that reason was refused by Kosztolanyi, who kept the manuscript, annotated by him, so that it can be made public only after his death. The name of the author became known at that time.