Applications of Direct Lyapunov Method in Caputo Non-Integer Order Systems

Jerzy Baranowski; Marta Zagorowska; Waldemar BauerTomasz DziwinskiPawel Piatek

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Applications of Direct Lyapunov Method in Caputo Non-Integer Order Systems

机译：直接李雅普诺夫方法在Caputo非整数阶系统中的应用

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Paper presents certain properties of Lyapunov direct method for non-integer order systems. Mittag-Leffler stability is defined and its relationship with Lyapunov stability is investigated. General results for Lyapunov functions are presented and a new result allowing constructive stability analysis is proved. Results are illustrated with the examples of stability analysis for problem of cooling, chemical reaction evolution and parametric stability analysis.

机译：本文介绍了李雅普诺夫直接方法在非整数阶系统中的某些性质。定义了Mittag-Leffler稳定性，并研究了其与Lyapunov稳定性的关系。给出了李雅普诺夫函数的一般结果，并证明了允许建设性稳定性分析的新结果。通过冷却问题的稳定性分析、化学反应演化和参数稳定性分析等实例对结果进行了说明。

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《Electronics and Electrical Engineering》 |2015年第2期|10-13|共4页
作者
Jerzy Baranowski; Marta Zagorowska; Waldemar BauerTomasz DziwinskiPawel Piatek;
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AGH University of Science and Technology;

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原文格式 PDF
正文语种英语
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关键词
Command and control systems; stability; stability criteria; Lyapunov methods; fractional calculus;

机译：指挥和控制系统;稳定性;稳定性标准;李雅普诺夫方法;分数阶微积分;

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1. Application of lyapunov's direct method to the investigation of the global stability of the solutions of systems with impulse effect [J] . Georgi Kulev, Drumi Bainov applicable analysis . 1988,第4期

机译：Application of lyapunov's direct method to the investigation of the global stability of the solutions of systems with impulse effect
2. A complete result on the Lyapunov stability of Caputo fractional-order nonautonomous systems by the comparison method [J] . Wu Cong Nonlinear dynamics . 2021,第3期

机译：A complete result on the Lyapunov stability of Caputo fractional-order nonautonomous systems by the comparison method
3. External stability of Caputo fractional-order nonlinear control systems: advances in the Lyapunov function method [J] . Wu Cong Nonlinear dynamics . 2021,第1期

机译：External stability of Caputo fractional-order nonlinear control systems: advances in the Lyapunov function method
4. Overpressure Protection of a Pressure Vessel by System Design through the Application of ASME VIII UG-140 in lieu of a Relief device by an Appropriate Choice of MAWP and/or by Safety Instrumented System [C] . Dilip K. Das Global Congress on Process Safety . 2015

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5. Statistical Methods for Wearable Device Data: Applications in Clinical Studies =可穿戴设备数据的统计分析方法及其在临床研究中的应用 [D] . Li, Xinyue. 2019

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6. Lyapunov-type inequalities for an anti-periodic fractional boundary value problem involving ψ-Caputo fractional derivative [O] . Bessem Samet, Hassen Aydi -1

机译：ψ-Caputo分数阶导数的反周期分数边值问题的Lyapunov型不等式
7. Application of SWOT Method to Evaluate the Feasibility Study on Land Treatment System of Rural Wastewater [O] . Fu-Hung Tso, Chen-Jung Liu, Paris Honglay Chen, 2014

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8. Hybrid Patterson-Superposition/Direct-Method Approach to the X-Ray Phase Problem, and in-Lab EXAFS Techniques [R] . Wang Lii, S. L. 1986

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Applications of Direct Lyapunov Method in Caputo Non-Integer Order Systems

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