5 CONCLUSIONS
A sufﬁcient LMI condition for robust quadratic stabi-
lization of polynomial systems under nonlinear per-
turbations has been proposed in this work. This new
feedback stabilizing approach is based on the direct
Lyapunov method and elaborated algebraic develop-
ments using the Kronecker product properties. These
developments have been turned into an LMI min-
imization problem, which can be easily solved by
means of numerically efﬁcient convex programming
algorithms. A mono-machine power system is consid-
ered as an application example of the technique devel-
oped in this paper. The numerical simulation results
have conﬁrmed the efﬁciency of the proposed poly-
nomial controller which can rapidly damp the system
oscillations and greatly enhance the transient stability
of the considered mono-machine power system de-
spite the nonlinear uncertainty affecting the studied
system.
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