Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function


CİVELEK C., CİHANBEĞENDİ Ö.

FRONTIERS OF INFORMATION TECHNOLOGY & ELECTRONIC ENGINEERING, vol.21, no.4, pp.629-634, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1631/fitee.1900014
  • Journal Name: FRONTIERS OF INFORMATION TECHNOLOGY & ELECTRONIC ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC
  • Page Numbers: pp.629-634
  • Keywords: Lyapunov function, Residual energy function, Stability of dissipative gyroscopic system, 0313, HAMILTONIAN-SYSTEMS, STABILITY
  • Dokuz Eylül University Affiliated: Yes

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.