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The Lyapunov functionVand its time derivativeV̇are expressed in matrix form byx'Sxandx'Tx, respectively, whereSandTcontain elements which involve the state variables, andx'is the transpose ofx. A given fourth-order nonlinear system is characterized byẋ=A(x)x, whereA(x)contains nonlinear elements. Simanov's problem is extended to a fourth-order system whose nonlinearity is a constrained function of two state variables.
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Y. Ku (1964) studied this question.
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