LMIs in Control/Stability Analysis/Lyapunov LMI

LMIs in Control/Stability Analysis/Lyapunov LMI

The System:

$\begin{array}{cc}\dot{x}(t)& =Ax(t)\\ x(0)& =x_0\end{array}$

The Optimization Problem:

The LMI: The Lyapunov Inequality

$\begin{array}{cc}\text{Find}X:& \\ \left[\begin{array}{c}X\end{array}\right]& >0\\ \left[\begin{array}{c}{A}^{T}X+XA\end{array}\right]& <0\end{array}$

Conclusion:

If feasible, System is internally exponentially Stable for any $x_0\in {ℝ}^n$.

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