Discrete Lyapunov function by means of a discrete residual energy
function and stability analysis for discrete time physical systems
Abstract
In this research paper beginning from the fundamental concepts, all the
basic approach is introduced for short. Then after obtaining the
discrete Lagrange-dissipative model ({L,D}- model for short) of a
discrete time observed physical/engineering dynamic system, the model
will be used to develope the discrete Hamiltonian together with discrete
dissipation energy as discrete Lyapunov function and as such, a
systematic method is proposed to obtain discrete Lyapunov function in
form of a residual energy function for discrete (time) observed physical
systems to analyze the discrete time system related to stability.
Stability analysis of a discrete time observed physical dynamic system
is performed using discrete Lyapunov function in form of a residual
energy function consisting of Hamiltonian together with dissipation
energy. Application of the method was shown using two discrete time
physical examples, one of which is a coupled one and time dependent.
This coupled physical discrete time example is analyzed related to
stability using two different formulations, one form of which leads to a
result.