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Frontiers of Information Technology & Electronic Engineering
ISSN 2095-9184 (print), ISSN 2095-9230 (online)
2020 Vol.21 No.4 P.629-634
Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function
Abstract: In a dissipative gyroscopic system with four degrees of freedom and tensorial variables in contravariant (right upper index) and covariant (right lower index) forms, a Lagrangian-dissipative model, i.e., {L, D}-model, is obtained using second-order linear differential equations. The generalized elements are determined using the {L, D}-model of the system. When the prerequisite of a Legendre transform is fulfilled, the Hamiltonian is found. The Lyapunov function is obtained as a residual energy function (REF). The REF consists of the sum of Hamiltonian and losses or dissipative energies (which are negative), and can be used for stability by Lyapunov’s second method. Stability conditions are mathematically proven.
Key words: Lyapunov function, Residual energy function, Stability of dissipative gyroscopic system
Cem CİVELEK1, Özge CİHANBEĞENDİ2
1埃格大学电气与电子工程系工程学部，土耳其伊兹密尔博尔诺瓦，35100
2度库兹•埃路尔大学电气与电子工程系工程学部，土耳其伊兹密尔布卡，35160
摘要：在自由度为4、张量有逆变（右上标）和协变（右下标）形式的耗散陀螺系统中，使用二阶线性微分方程建立拉格朗日耗散模型，即{L, D}模型。通过系统的{L, D}模型确定广义元素。满足勒让德变换先决条件时，可得哈密顿量。剩余能量函数（REF）由哈密顿量及损耗或耗散能量（为负）之和组成，将其作为李雅普诺夫函数，可通过李雅普诺夫第二方法作稳定性分析，并从数学上推导出稳定性条件。
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DOI:
10.1631/FITEE.1900014
CLC number:
O313
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On-line Access:
2020-04-21
Received:
2019-01-10
Revision Accepted:
2019-05-25
Crosschecked:
2020-03-06