Constructing Lyapunov functions for certain fourth-order autonomous differential equations
type: Item
instance of: scholarly article
title: Constructing Lyapunov functions for certain fourth-order autonomous differential equations
zbMATH Open document ID: 0828.34043
author: Cemil Tunç
author: Aydin Tiryaki
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1996-01-02T00:00:00Z
review text: Using the so-called intrinsic method introduced by \textit{P. S. M. Chin} [Int. J. Control 48, No. 4, 1561-1567 (1988; Zbl 0653.93038)] the author constructs Lyapunov functions for the autonomous fourth-order equations \(x^{(4)}+ a_1 x^{(3)}+ f(x, \dot x) \ddot x+ a_3 \dot x+ h(x)= 0\) and \(x^{(4)}+ a_1 x^{(3)}+ f(x, \dot x)\ddot x+ g(\dot x)+ a_4 x= 0\). The stability conditions obtained from these functions are weaker than those presented earlier by M. L. Cartwright, J. O. C. Ezeilo, and A. S. Skidmore.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 790820
zbMATH Keywords: intrinsic method
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: autonomous fourth-order equations
zbMATH Keywords: stability conditions
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description: scientific article; zbMATH DE number 790820