Constructing Lyapunov functions for certain fourth-order autonomous differential equations
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.
scientific article; zbMATH DE number 790820
scientific article