LMIs in Control/Stability Analysis/LMI for the Controllability Grammian

This is a Template for Creating An LMI Page

The System


\begin{align} \dot x(t)&=Ax(t)+B_pp(t)+B_ww(t),\\ z(t)&=C_zx(t)\\ p_i(t)&=\phi_i(q_i(t)), i=1,\dots, n_p\\ q&=C_qx,\\ 0 &\leq \sigma \phi_i(\sigma) \leq \sigma^2 \ \forall \sigma \in \mathbb{R} \end{align}$$

The Data
The matrices $$ A,B_p,B_w,C_q,C_z $$.

The LMI: The Lyapunov Inequality
Title and mathematical description of the LMI formulation.



\begin{align} \text{Find} \; &P>0,\Lambda=diag(\lambda_1,\dots,\lambda_{n_p}), T=diag(\tau_1):\\ \begin{bmatrix} X\end{bmatrix}&>0\\ \begin{bmatrix} A^T X+XA\end{bmatrix}&<0 \end{align}$$

Conclusion:
Interpretation of the results of the LMI

Implementation
A link to CodeOcean or other online implementation of the LMI

Related LMIs
Links to other closely-related LMIs