Lyapunov function of a fourth-order system

The Lyapunov functionVand its time derivativedot{V}are 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 bydot{x}=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.