Lyapunov function of a fourth-order system

The Lyapunov function
V
and its time derivative
\dot{V}
are expressed in matrix form by
x'Sx
and
x'Tx
, respectively, where
S
and
T
contain elements which involve the state variables, and
x'
is the transpose of
x
. A given fourth-order nonlinear system is characterized by
\dot{x}=A(x)x
, where
A(x)
contains nonlinear elements. Simanov's problem is extended to a fourth-order system whose nonlinearity is a constrained function of two state variables.