Applied sciences

Bulletin of the Polish Academy of Sciences Technical Sciences

Content

Bulletin of the Polish Academy of Sciences Technical Sciences | 2026 | 74 | 3

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Abstract

In this paper, we utilize matrix transformations and inequalities to derive a novel upper bound and two lower bounds to solve the unified algebraic Lyapunov matrix equation (UALE). We then review existing bounds for the UALE and compare them with our new bounds, highlighting that our upper bound is the least restrictive among current results. The restrictions of our newly established lower bound are either weaker than the existing lower bounds or consistent with them. Our upper and lower bounds demonstrate increased accuracy over existing results through some numerical examples. As an application to linear systems, we illustrate how our upper bound can be employed to analyze the robust stability of the unified system based on the delta operator. Finally, we validate the effectiveness and superiority of our results through a series of numerical examples.
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Authors and Affiliations

Yan Xu
1
Jianzhou Liu
1
ORCID: ORCID

  1. School of Mathematics and Computational Science & Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,Xiangtan University, Xiangtan, Hunan, 411105, PR China
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Abstract

Fast convergence is one of the core pursuit goals of modern high-performance control systems. This article investigates the fast convergence control problem of Markov jump systems. In order to ensure the feasibility of the fast convergence controller design method, the Lyapunov-Krasovskii functional is constructed based on Lyapunov stability theory in the derivation process of the algorithm. Based on a time-varying proportional function, a distributed control algorithm is designed and the fast convergence controller design method is proposed for the considered systems. The variation of controller gain with time is discussed in sections, and the boundary of controller output is given to make the designed controller more practical for real-world engineering applications. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed method in this paper.
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Authors and Affiliations

Bo Li
1
ORCID: ORCID
Junjie Zhao
1
Xuejing Ren
2

  1. School of Electrical and Information Engineering, Jiangsu University of Technology, 1801 Zhongwu Road, Changzhou, Jiangsu, China
  2. School of Science, Changzhou Institute of Technology, 666 Liaohe Road, Changzhou, Jiangsu, China
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Abstract

The paper presents results of an investigation into a gas-delayed blowback operation firearm system. A recently developed experimental stand was used to this end. In this article, the results are subjected to statistical analysis using design of experiments methods, including response surface methodology (RSM). This analysis facilitates the determination of the significance and nature of parameters such as distance of the gas port from the breech end of the barrel, diameter of the gas port, mass of the recoiling assembly, diameter of the gas piston rod and length of the gas chamber that influence the operation of such systems. The results of the research can be used to validate a mathematical model of a weapon operating on this principle and serve as the starting point for the optimization process of this type of design.
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Authors and Affiliations

Dawid Goździk
1
ORCID: ORCID
Mateusz Morawski
1
ORCID: ORCID
Ryszard Woźniak
1
ORCID: ORCID
Mirosław Zahor
1
ORCID: ORCID
Radosław Trębiński
1
ORCID: ORCID

  1. Military University of Technology, Faculty of Mechatronics, Armament and Aerospace, ul. Kaliskiego 2, 00-908 Warsaw, Poland
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Abstract

This study proposes a method for estimating vehicle load using sinusoidal steering excitation and analysis of dynamic responses: lateral velocity (LV), roll velocity (RV) and yaw velocity (YV). The approach enables reliable discrimination between unloaded (W1) and loaded (W2) vehicle states under real driving conditions. Lateral velocity increases with vehicle speed and exhibits higher magnitudes for the loaded state, particularly within the 0.5–1.5 Hz range. Phase responses for W2 show stronger negative shifts and earlier transitions, indicating increased dynamic delay, which makes LV a useful supplementary indicator, especially at medium speeds. Roll velocity (RV) is identified as the most sensitive and repeatable response, and serves as the primary diagnostic variable. The largest differences between loading states occur within the 0.9–1.3 Hz range, where W2 responses exhibit higher amplitudes and a shift toward lower frequencies, directly reflecting increased vehicle mass. Above 2 Hz, system damping increases and load-related differences diminish. Yaw velocity (YV) shows amplitudes 1–3 dB higher for W2 within the 0.6–1.6 Hz range, together with phase shifts, but its sensitivity is lower than that of RV, classifying it as a supplementary indicator. Unlike methods based on complex identification algorithms or high-frequency measurements, this study adopts a simplified linear single-degree-of-freedom (1-DoF) oscillator model. Defined road-test conditions, including speeds of 45–56 km/h and excitation near 1.0 Hz, ensure dominance of a single dynamic mode. The method is computationally efficient and cost-effective, although its linear formulation may limit accuracy under strongly nonlinear dynamics or varying road conditions.
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Authors and Affiliations

Tomasz Pusty
1
ORCID: ORCID
Marcin Mieteń
1
Włodzimierz Kupicz
1

  1. The Military Institute of Armoured and Automotive Technology, 05-070 Sulejówek k. Warszawy, Poland

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NEW PUBLICATION FEES
Articles submitted by December 31st, 2024: existing fee: 1500 PLN (and mandatory over-length charges of 230 PLN per page)
Articles submitted from January 1st, 2025: new fee: 2000 PLN (approx. 500 EUR- depending on the exchange rate) - a flat fee per paper up to 8 pages of the journal format (each additional page will be charged an additional 250 PLN).

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