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Engineering: Lyapunov Functions
Engineering and Construction
Pages 4 (1004 words)
Lyapunov Function Student`s Name Institution of Learning: Instructor`s Name; Course Name: Date of Submission Lyapunov Function Introduction With reference to the ordinary differential equations (ODEs) theory, Lyapunov functions can be defined as scalar functions that are normally used in proving equilibrium stability on a given ODE.
For a number of ODEs classes, the presence of Lyapunov functions is considered as being a sufficient and necessary stability condition. Now that there are no general formulae of coming up with ODE’s Lyapunov functions, in most cases, the construction of these functions are normally known (Burton, 2002). Lyapunov functions can also be looked at in an informal perspective in that it takes values that are positive in every situation except for the values at the equilibrium after which it either increases or decreases following an ODE trajectory. The Lyapunov functions principle merit based on the analysis of stability of ODEs states that the definite solution of the ODE is not necessary -be it numerical or analytical (Aydin and Bulgak, 2004). History Lyapunov function of control was named after Mikhailovich Lyapunoy. Lyapunoy was the first mathematician to take interest in possible modifications of nonlinear systems in relation to the linear stability theory with the equilibrium point being his point of reference. For many years, his work got minimal attention. It was after the Cold War that most people suddenly started getting interested in his work as they realized it was applicable in aerospace stability guidance system. This system initially had several nonlinearities which could not be solved by other methods. ...
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