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

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

This is a Template for Creating An LMI Page

The System

$\begin{array}{cc}\dot{x}(t)& =Ax(t)+B_{p}p(t)+B_{w}w(t),\\ z(t)& =C_{z}x(t)\\ p_i(t)& ={\varphi }_i(q_i(t)),i=1,\dots ,n_p\\ q& =C_{q}x,\\ 0& \le \sigma {\varphi }_i(\sigma )\le {\sigma }^2\mathrm{\forall }\sigma \in ℝ\end{array}$

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.

$\begin{array}{cc}\text{Find}& P>0,\mathrm{\Lambda }=diag({\lambda }_1,\dots ,{\lambda }_{n_p}),T=diag({\tau }_1):\\ \left[\begin{array}{c}X\end{array}\right]& >0\\ \left[\begin{array}{c}{A}^{T}X+XA\end{array}\right]& <0\end{array}$

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

External Links

A list of references documenting and validating the LMI.

• LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
• LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
• LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.