http://hdl.handle.net/10563/1000007 Sat, 02 May 2026 03:25:54 GMT 2026-05-02T03:25:54Z http://hdl.handle.net/10563/1012806 Necessary and sufficient condition for existence of two-degree-of-freedom feedback loop factorisation and comparison of zeros in compensator strategies Dlapa, Marek; Pekař, Libor Two cases of the two-degree-of-freedom (2DOF) feedback loop are compared after applying them to the third-order system with uncertain time delay, the fourth-order system with astatism and uncertain time delay and the oscillating system with astatism and uncertain time delay. All systems have periodic changes of some of their parameters. The necessary and sufficient condition for the existence of 2DOF factorisation is formed and proven. The uncertain time delay is treated using multiplicative uncertainty; the periodic changes of parameters are modelled using a general interconnection for the systems with parametric uncertainty in the numerator and denominator. The structured singular value denoted μ is used as a measure of robust performance and stability. For comparison, the D-K iteration and algebraic μ-synthesis are used for simple feedback loop controller derivation. The algebraic μ-synthesis is a new method for robust controller derivation comprising the structured singular value, algebraic control theory and metaheuristic algorithm solving multimodality of the cost function. Minimisation of the μ-function in the algebraic μ-synthesis is treated using the Differential Migration algorithm as a tool for global optimisation with subsequent tune-up using the Nelder–Mead simplex method. The final controllers are verified using the μ-plots and simulations for the worst-case perturbation and periodic changes of parameters with the maximum time delay. © 2026 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Thu, 01 Jan 2026 00:00:00 GMT http://hdl.handle.net/10563/1012806 2026-01-01T00:00:00Z http://hdl.handle.net/10563/1012778 Complete stability analysis and optimal design for dual-state-feedback delayed resonator Gao, Qingbin; Cai, Jiazhi; Wu, Hao; Zhou, Kai; Pekař, Libor We propose a dual-state-feedback delayed resonator (DFDR) by incorporating an additional acceleration-based feedback into the classical DR design. The optimal tuning of its feedback parameters is guided by two objectives: enhancing vibration suppression at a specified target frequency and maintaining overall system stability. First, we extend the Advanced Clustering with Frequency Sweeping (ACFS) methodology from the delay-only domain to the combined delay-gain domain, enabling a rigorous and complete stability analysis where feedback gains and delays interact. Second, we develop the optimal parameter tuning procedure and demonstrate that the proposed DFDR achieves improved stability margins, enhanced robustness to frequency variations, and superior vibration suppression performance compared to the classical DR. These results highlight the practical potential of DFDR as an effective and robust solution for active vibration suppression systems. Thu, 01 Jan 2026 00:00:00 GMT http://hdl.handle.net/10563/1012778 2026-01-01T00:00:00Z http://hdl.handle.net/10563/1012779 A purely algebraic proof of the omega-reducibility of pseudovarieties representing low half levels of concatenation hierarchies Volaříková, Jana We are concerned with the ω-reducibility of pseudovarieties of ordered monoids representing half levels of concatenation hierarchies. In the author’s paper (Int. J. Algebra Comput. 64(01), 87–135, 2024), the ω-reducibility of pseudovarieties representing levels 1/2 and 3/2 of concatenation hierarchies with a locally finite basic pseudovariety has been proven, using results of the paper by Place (Log. Methods Comput. Sci. 14(4:16), 1–58, 2018) on so called covering of corresponding sets of regular languages. In this paper, we prove the same results on the ω-reducibility, not using the results of the mentioned paper by Place, although still inspired by their proofs. This new method of the proofs of the ω-reducibility prepares us to their potential extension to higher half levels of concatenation hierarchies. The process of a gradual generalization is initiated in this paper. Thu, 01 Jan 2026 00:00:00 GMT http://hdl.handle.net/10563/1012779 2026-01-01T00:00:00Z http://hdl.handle.net/10563/1012774 Additively transtable conic sections with respect to fixed coefficients Cerman, Zbyněk; Vítková, Lenka The arithmetic mean has several important properties. One of them preserves the result of the arithmetic mean. That is, if one value increases and another decreases, the result of the arithmetic mean is the same. This property is called transfer stability, transtability for short. We can see its reach in several mathematical theories. The most common use is with aggregation functions. This article aims to show another use of this property, specifically in the geometry of conic sections. We have outlined how the transtability of a conic section works. The main idea was to find a common property for conic sections connected by transtability. We found that these conics have the same common intersection and the set of all centers forms a conic. Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10563/1012774 2025-01-01T00:00:00Z