LMIs in Control/Stability Analysis/Lyapunov LMI

LMIs in Control/Stability Analysis/Lyapunov LMI

The System:

${\begin{aligned}{\dot {x}}(t)&=Ax(t)\\x(0)&=x_{0}\end{aligned}}$

The Optimization Problem:

The LMI: The Lyapunov Inequality

${\begin{aligned}{\text{Find}}\;X:&\\{\begin{bmatrix}X\end{bmatrix}}&>0\\{\begin{bmatrix}A^{T}X+XA\end{bmatrix}}&<0\end{aligned}}$

Conclusion:

If feasible, System is internally exponentially Stable for any $x_{0}\in \mathbb {R} ^{n}$.

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