User:Margav06/sandbox/Click here to continue/LMIs in system and stability Theory/Continuous- time Lyapunov Stability

The System:



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

The Optimization Problem:

The LMI: The Lyapunov Inequality

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

Conclusion:

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

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