OpenLLM-France/wikimedia huggingface dataset:
# LMIs in Control/Matrix and LMI Properties and Tools/Dualization Lemma
## Dualization Lemma

Consider $P_{i}\in {\text{S}}^{n}$ and the subspaces $U,V$, where $P$ is invertible and $U+V={\text{R}}^{n}$. The following are equivalent.
$X^{T}PX<0$ for all $X\in {\text{U}}$\$\left\{0\right\}$ and $X^{T}PX\geq 0$ for all $X\in {\text{V}}$.
$X^{T}P^{-1}X>0$ for all $X\in {\text{U}}^{\bot }$\$\left\{0\right\}$ and $X^{T}P^{-1}X\leq 0$ for all $X\in {\text{V}}^{\bot }$.

## Example

Consider the matrices $Q\in {\text{S}}^{n},S\in {\text{R}}^{n\times m},R\in {\text{S}}^{m},M\in {\text{R}}^{m\times n}$ where $R\geq 0,$ which define the quadratic matrix inequality
${\begin{aligned}\qquad {\begin{bmatrix}1&M\\\end{bmatrix}}{\begin{bmatrix}Q&S\\S^{T}&R\\\end{bmatrix}}{\begin{bmatrix}1\\M\\\end{bmatrix}}<0.\qquad (1)\end{aligned}}$
Define ${\begin{aligned}P={\begin{bmatrix}Q&S\\S^{T}&R\\\end{bmatrix}},U=R({\begin{bmatrix}0\\1\\\end{bmatrix}})\end{aligned}}$ where $U+V=R^{n+m}$. Notice that $(1)$ is equivalent to $X^{T}PX<0$ for all $X\in {\text{U}}$\$\left\{0\right\}$.Additionally, $X^{T}PX<0\geq$ for all $X\in {\text{V}}$ is euaivalent to
${\begin{aligned}\qquad {\begin{bmatrix}0&1\\\end{bmatrix}}{\begin{bmatrix}Q&S\\S^{T}&R\\\end{bmatrix}}{\begin{bmatrix}0\\1\\\end{bmatrix}}=R\geq 0,\end{aligned}}$
which is satisfied based on the definition of $R$ . By the dualization lemma, $(1)$ is satisfied with $R\geq 0$ if and only if
${\begin{aligned}\qquad {\begin{bmatrix}-M^{T}&1\\\end{bmatrix}}{\begin{bmatrix}{\tilde {Q}}&{\tilde {S}}\\{\tilde {S}}^{T}&{\tilde {R}}\\\end{bmatrix}}{\begin{bmatrix}-M^{T}\\1\\\end{bmatrix}}>0,\qquad {\tilde {Q}}\leq 0,\end{aligned}}$
where ${\begin{aligned}\qquad {\begin{bmatrix}{\tilde {Q}}&{\tilde {S}}\\{\tilde {S}}^{T}&{\tilde {R}}\\\end{bmatrix}}={\begin{bmatrix}Q&S\\S^{T}&R\\\end{bmatrix}}^{-1},U^{\bot }=N([1\quad M^{T}])=R({\begin{bmatrix}-M^{T}\\1\\\end{bmatrix}})\end{aligned}}$ , and ${\begin{aligned}V^{\bot }=N([0\quad 1])=R({\begin{bmatrix}1\\0\\\end{bmatrix}})\end{aligned}}$.

## External Links

* 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.
* Norm-Preserving Dilations - Norm-preserving dilations and their applications to optimal error bounds (Davis, Kahan, Weinberger).
# LMIs in Control/Matrix and LMI Properties and Tools/Generalized H2 Norm
## Generalized $H_{2}$ Norm

The $H_{2}$ norm characterizes the average frequency response of a system. To find the H2 norm, the system must be strictly proper, meaning the state space represented $D$ matrix must equal zero. The H2 norm is frequently used in optimal control to design a stabilizing controller which minimizes the average value of the transfer function, $G$ as much as possible. This optimal control problem is also called the Linear Quadratic Gaussian.

## The System

Consider a continuous-time, linear, time-invariant system $G:L_{2e}\to L_{2e}$ with state space realization $(A,B,C,0)$ where $A\in \mathbb {R} ^{n\times n}$, $B\in \mathbb {R} ^{n\times m}$, $C\in \mathbb {R} ^{p\times n}$, amd $A$ is Hurwitz. The generalized $H_{2}$ norm of $G$ is:
$\left\|G\right\|_{2,{\infty }}=\sup _{u\in L_{2},{u}\neq {\text{zero}}}$ ${\frac {\left\|Gu\right\|_{\infty }}{\ \left\|u\right\|_{2}}}$

## The Data

The transfer function $G$, and system matrices $A$, $B$, $C$ are known and $A$ is Hurwitz.

## The LMI: Generalized $H_{2}$ Norm LMIs

The inequality $\left\|G\right\|_{2,{\infty }}<\mu$ holds under the following conditions:
1. There exists $P\in \mathbb {S} ^{n}$ and $\mu \in \mathbb {R} _{>0}$ where $P>0$ such that:
       ${\begin{bmatrix}A^{T}P+PA&PB\\*&-\mu 1\end{bmatrix}}<0$.
       ${\begin{bmatrix}P&C^{T}\\*&\mu 1\end{bmatrix}}>0$.
2. There exists $Q\in \mathbb {S} ^{n}$ and $\mu \in \mathbb {R} _{>0}$ where $Q>0$ such that:
       ${\begin{bmatrix}QA^{T}+AQ&B\\*&-\mu 1\end{bmatrix}}<0$.
       ${\begin{bmatrix}Q&QC^{T}\\*&\mu 1\end{bmatrix}}>0$.
3. There exists $P\in \mathbb {S} ^{n},V\in \mathbb {R} ^{n\times n}$ and $\mu \in \mathbb {R} _{>0}$ where $P>0$ such that:
       ${\begin{bmatrix}-(V+V^{T})&V^{T}A+P&V^{T}B&V^{T}\\*&-P&0&0\\*&**-\mu 1&0\\*&*&*&-P\end{bmatrix}}<0$.
       ${\begin{bmatrix}P&C^{T}\\*&\mu 1\end{bmatrix}}>0$.

## Conclusion:

The generalized $H_{2}$ norm of $G$ is the minimum value of $\mu \in \mathbb {R} _{>0}$ that satisfies the LMIs presented in this page.

## Implementation

This implementation requires Yalmip and Sedumi.
Generalized $H_{2}$ Norm - MATLAB code for Generalized $H_{2}$ Norm.

## Related LMIs

LMI for System H_{2} Norm

## External Links

* 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.
* LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013.

## Return to Main Page:

LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control
# LMIs in Control/Matrix and LMI Properties and Tools/Discrete Time

      * Discrete Time H2 Norm
      * Discrete Time Minimum Gain Lemma
      * Modified Discrete Time Minimum Gain Lemma
      * Discrete-Time Algebraic Riccati Equation
      * Discrete-Time Negative Imaginary Lemma
      * Discrete-Time System Zeros with Feedthrough
# LMIs in Control/Matrix and LMI Properties and Tools/Ellipsoidal inequality
## Introduction

The simplex algorithm was the first algorithm proposed for linear programming, and although the algorithm is quite fast in practice, no variant of it is known to be polynomial time. The Ellipsoid algorithm is the first polynomial-time algorithm discovered for linear programming. The Ellipsoid algorithm was proposed by the Russian mathematician Shor in 1977 for general convex optimization problems and applied to linear programming by Khachyan in 1979.
The Ellipsoidal inequality constraints are a type of Lyapunov Function. They are important in process identification, parameter estimation, and statistics. Applications include the crystallization process, polymer film extrudes, and paper machines.

## The Data

Formulation of the inequality depends upon the coordinates of the ellipsoid $(x_{i})$ and the centre of the ellipsoid $(x_{c})$.

## The Ellipsoidal Inequality

An Ellipsoid is described by:
${\begin{aligned}\ (x-x_{c})^{T}P^{-1}(x-x_{c})<1,\\\ where,P=P^{T}>0\\\end{aligned}}$
It can be expressed as an LMI using the Schur complement lemma with $Q(x)=1,R(x)=P,andS(x)=(x-x_{c})^{T}:$
${\begin{bmatrix}1&&(x-x_{c})^{T}\\(x-x_{c})&&P\end{bmatrix}}$ ${\begin{aligned}\geq 0\end{aligned}}$

## Conclusion

Using this inequality, as the algorithm advances to the next step; if the value of P is positive; the volume will keep on shrinking until the LMI is fulfilled.

## Implementation

* https://github.com/Margav06/LMI-for-Ellipsoidal-Inequality

## External Links

A list of references documenting and validating the LMI.
* https://web.mit.edu/braatzgroup/33_A_tutorial_on_linear_and_bilinear_matrix_inequalities.pdf
* http://www-math.mit.edu/~goemans/18433S09/ellipsoid.pdf

## Return to Main Page

https://en.wikibooks.org/wiki/LMIs_in_Control
# LMIs in Control/Matrix and LMI Properties and Tools/Finsler's Lemma

LMIs in Control/Matrix and LMI Properties and Tools/Finsler's Lemma
This method It states equivalent ways to express the positive definiteness of a quadratic form Q constrained by a linear form L. It is equivalent to other lemmas used in optimization and control theory, such as Yakubovich's S-lemma, Finsler's lemma and it is wedely used in Linear Matrix Inequalities

## Theorem

Consider $\Psi \in \mathbb {S} ^{n},G\in \mathbb {R} ^{n\times m},\mathrm {A} \in \mathbb {R} ^{m\times p},H\in \mathbb {R} ^{n\times p}$and $\sigma \in \mathbb {R}$. There exists $\mathrm {A}$ such that
$\Psi +G\mathrm {A} H^{T}+H\mathrm {A} ^{T}G^{T}<0,$
if and only if there exists $\sigma$ such that
$\Psi -\sigma GG^{T}<0$
$\Psi -\sigma HH^{T}<0$

## Alternative Forms of Finsler's Lemma

Consider $\Psi \in \mathbb {S} ^{n},Z\in \mathbb {R} ^{p\times n},x\in \mathbb {R} ^{n}$and $\sigma \in \mathbb {R} _{>0}$. If there exists $Z$ such that
$x^{T}\Psi x,0$
holds for all $x$ ≠ $0$ satisfying $Zx=0$, then there exists $\sigma$ such that
$\Psi -\sigma Z^{T}Z<0$

## Modified Finsler's Lemma

Consider $\Psi \in \mathbb {S} ^{n},G\in \mathbb {R} ^{n\times m},\mathrm {A} \in \mathbb {R} ^{m\times p},H\in \mathbb {R} ^{n\times p}$and $\epsilon \in \mathbb {R} _{>0}$, where $\mathrm {A} ^{T}\mathrm {A}$ is less that on equal to $\mathbb {R}$, and $R>0$. There exists $\mathrm {A}$ such that
$\Psi +G\mathrm {A} H^{T}+H\mathrm {A} ^{T}G^{T}{T}<0,$
there exists $\epsilon$ such that
$\Psi +\epsilon ^{-1}GG^{T}+\epsilon HRH^{T}<0.$

## Conclusion

In summary, a number of identical methods have been stated above to determine the positive definiteness of 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.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.
# Knowing Knoppix/Recovering from freezes

It is possible for the X Window System, the K Desktop Environment, or an individual application to "freeze up". This section explains what to do if that happens.

## Getting rid of an individual application

The most common situation is to have a program that just doesn't seem to want to go away. Even when you click the close button on its window, it still won't disappear. To get rid of it:
* Press Ctrl+Alt+Esc on the keyboard.
* The pointer will change into a skull and crossbones.
* Point anywhere inside the window that you want to get rid of.
* Click the left mouse button.
* The errant program will be killed.

## Restarting the X Window System

If many programs or your entire graphical environment seems stuck, you can try to restart the X server entirely.
Pressing Ctrl-Alt-Backspace kills X. The display manager should bring it back up again.
An alternate way to restart X in Knoppix is to:
* Press Ctrl+Alt+F2.
* Type this command, then press Enter: init 2
* You will see the message "X Window System shut down". This will also end the K Desktop Environment and all its open applications.
* Then enter: init 5
* The X Window System will be restarted. The KDE desktop will appear again as it did when you first started Knoppix.
# Miskito/History

| Contributors | Project history |
| > Next | Project history |
| Contents | |

## Announcing the project

I am bringing on line this project, which I have recently been preparing and which will grow over coming days and weeks according to unfolding plans. Please refer to the contents page to see existing components and the course's structure and makeup (further explanations will follow as time permits). Contributions and comments are of course very welcome. I will add to or reformulate this page as the project progresses. Wish me luck! --A R King 08:10, 26 January 2007 (UTC)

## New page log

The page log page is now here.

## Latest news

Only three weeks after starting the project, the first ten lessons have been completed together with many complementary pages and full development of almost the items in the Table of Contents. Work of the course is now sufficiently advanced to make it functional. Even I am amazed! The experiment has also shown that Wikibooks is a good platform for a production of this kind. There is still plenty more to do - the rest of the lessons, in particular. --A R King 10:04, 20 February 2007 (UTC)
Oops! I got sidetracked after this "experiment" and have failed to continue developing the course since then. Apologies for that. I only just found out it was featured last year, thanks everyone who was responsible for that! --A R King (discuss • contribs) 09:20, 27 August 2011 (UTC)
# Miskito/Contents

| Lesson 1 | Table of Contents |
| > Next | Table of Contents |
| Contents | |
| Getting started Miskitu aisas! Welcome to Miskitu Aisas! · The Miskito people and their language · How to use the course · Where to next? Pronunciation and spelling Vowels · Consonants · Semivowels and diphthongs · Accent and aspiration · Reading practice Lessons Lesson 1: Nini Mary sa (My name is Mary) is · this and that · the · a Lesson 2: Buk ba tibil ra sa (The book is on the table) In, on and at · Plural nouns · We, they, these and those · Isn't/aren't Lesson 3: Tawan ra sap kum bara sa ki? (Is there a shop in the village?) There is/are · Questions · Who, what and where · Your Lesson 4: Yaptiki ba Miskitu aisisa (My mother speaks Miskito) The -isa form · The -ras form Lesson 5: Naha wina Bilwi ra (From here to Bilwi) To and from · Here and there · Direct objects · A note on infinitives Lesson 6: Nahwala, yauhka (Yesterday, tomorrow) With · The future tense · The past tense Lesson 7: Inglis aisisma ki? (Do you speak English?) I am · You are · Some personal pronouns · The present tense · The future tense Lesson 8: Anira auma ki? (Where are you going?) Go, come, know, and want · The negative · Past forms Lesson 9: Wan skulka (Our school) The -ka ligature after demonstratives · Rules for adding -ka · Other uses of ligature · The genitive construction Lesson 10: Miskitu aisi banghwisna (We speak Miskito) Plural personal pronouns · Banghwaia · A-verbs and i-verbs · The -a or -ya ligature READING: Miskitu yumhpa MORE LESSONS REFERENCE SECTION MORE ABOUT MISKITO THE PROJECT | The project Authors and contributors Major authors · Further contributors Project history Announcing the project · New page log · Latest news Current development Setting up · "To do" list · Help needed! Aims and objectives Long-range goals / Objectives for this course Method Basic resources · Structural syllabus · Target lexicon · Lesson design · Choosing model sentences · Explaining grammar · Composing mini-exercises · Vocabulary control · Review exercises · Layout procedures Authors' workbench Proposed syllabus Lesson-by-lesson list of planned structural content Planned lexicon A provisional word list Lesson structure How to start writing a lesson · Overall structure of a lesson · A note on layout · The model component · The exercise component · The commentary component · Vocabulary and review Layout guide Point layout · The model component · The exercise component · The commentary component · The vocabulary component · The review component Using the templates Template basics · Template index How to... start a new page · write a point · write a vocabulary/review section Page log Newly created pages are logged here Project note book Bits, pieces and snippets possibly of use later |
| More lessons Lesson 11: ? (?) (Coming soon!) Reference section Miskito-English vocabulary Covers the lessons so far written. English-Miskito vocabulary Covers lessons 1 to 10 Abbreviations used Subject index Appendix: Ligatures and possessive forms Appendix: Verb tables More about Miskito Miskito links and bibliography Miskito links · Bibliography Discussion page Your feedback please! ||
# Miskito/Contributors

| Discussion | Authors and contributors |
| > Next | Authors and contributors |
| Contents | |

## Major authors

* Major authors of this book: Would anyone considering themselves one of the main contributors to this book please place their information here.
* Enter "Edit" mode, make a new copy of the six lines beginning with double braces + "Miskito_Contributor" and ending with double braces; then fill in your data after the pipes on the middle four lines, which correspond to the four fields in the table.
| Name | Background/Qualifications | Contributions | Signature |
| Alan R King | Linguist, language teaching professional and specialist in minority and endangered languages. I have authored, designed and published several language course books. On Wikipedia I have written grammar sketches of several languages, including Miskito. | Designed the project, set a syllabus, programmed the roadmap, designed and created the first (model) pages, created templates, contents page, other pages, lesson pages. | --A R King 07:55, 26 January 2007 (UTC) |

## Further contributors

* Further contributors to this book: All others who have contributed in some way to this book are invited to place their information here.
* Enter "Edit" mode, make a new copy of the five lines beginning with double braces + "Miskito_Other_contributor" and ending with double braces; then fill in your data after the pipes on the middle three lines, which correspond to the three fields in the table.
| Name | Contributions | Signature |
# Dell Latitude D410
## CPU

* CPU: Intel Pentium M 730 1.6GHz

### Variations

* CPU: Intel Pentium M 750 1.86GHz
* CPU: Intel Pentium M 760 2.00GHz

## Memory

* Memory (Minimum): 256Mb (Shared)
* Memory Type: DDR2 400MHz or 533Mhz

## Video Graphics Display

* Video Graphics Chipset: Intel Graphics Media Accelerator 900 (128Mb shared)
* Screen Size: 12.1"
* Maximum Screen Resolution: XGA 1024 x 768

## Motherboard

* Chipset: Dell 915GM

## Hard Drive

* Minimum capacity: 30Gb

## Media Drives

* CDROM Drive: 24x CDROM

## Audio

* Audio Chipset:

## Network Ports

* 10/100/1000 Gigabit Ethernet LAN

## USB Ports

* USB 2.0 x 3

## Pointing Device

* Pointing Device Type: Touchpad PS/2 Compatible

### Variations

* Pointing Device Type: Unknown (Track Stick) PS/2 Compatible

### Wireless Networking

* Wifi Chipset: Dell 1450 802.11g Wireless

#### Variations

* Wifi Chipset: Intel 2200 wireless controller

### Open Source Compatibility

* Graphics Chipset: Yes (uses the i810 module)
* Audio: Yes (uses the snd-intel8x0 module)
* Ethernet: Yes
* Wireless: No (requires ndiswrapper)

#### Variations

Note that variations of this laptop contain an Intel 2200 Wifi chipset. The variant chipset does not require ndiswrapper and operates fine with the open source ipw2100 module).
# Dell Latitude D630
## CPU

* CPU:

## Memory

* Memory:
* Memory Type:

## Video Graphics Display

* Video Graphics Chipset: Nvidia Quattro NVS 135M (???Mb)
* Screen Size:
* Maximum Screen Resolution:

## Audio

* Audio Chipset:

## Pointing Device

* Pointing Device Type: Touchpad
# Dell Precision M4400
## CPU

* CPU:

## Memory

* Memory:
* Memory Type:

## Video Graphics Display

* Video Graphics Chipset: Nvidia Quadro FX770M (???MB)
* Screen Size:
* Maximum Screen Resolution:

## Audio

* Audio Chipset:

## Pointing Device

* Pointing Device Type: Touchpad
# Dell Latitude D400
## CPU

* CPU: Intel Pentium M 730 1.6GHz

### Variations

* CPU: Intel Pentium M 750 1.86GHz
* CPU: Intel Pentium M 760 2.00GHz

## Memory

* Memory (Minimum): 256Mb (Shared)
* Memory Type: DDR2 400MHz or 533Mhz

## Video Graphics Display

* Video Graphics Chipset: Intel Graphics Media Accelerator 900 (128Mb shared)
* Screen Size: 12.1"
* Maximum Screen Resolution: XGA 1024 x 768

## Motherboard

* Chipset: Dell 915GM

## Hard Drive

* Minimum capacity: 30Gb

## Media Drives

* CDROM Drive: 24x CDROM

## Audio

* Audio Chipset:

## Network Ports

* 10/100/1000 Gigabit Ethernet LAN

## USB Ports

* USB 2.0 x 3

## Pointing Device

* Pointing Device Type: Touchpad PS/2 Compatible

### Variations

* Pointing Device Type: Unknown (Track Stick) PS/2 Compatible

### Wireless Networking

* Dell 1450 802.11g Wireless

### Open Source Compatibility

Graphics Chipset: Yes (uses the i810 module) Audio: Yes (uses the snd-intel8x0 module) Ethernet: Yes Wireless: No (requires ndiswrapper)
# Dell Latitude D830
## CPU

* CPU:

## Memory

* Memory:
* Memory Type:

## Video Graphics Display

* Video Graphics Chipset: Nvidia Quattro NVS 135M (???Mb) (Some models have an Nvidia Quattro NVS 140M)
* Screen Size:
* Maximum Screen Resolution:

## Audio

* Audio Chipset:

## Pointing Device

* Pointing Device Type: Touchpad
# LMIs in Control/Click here to continue/LMIs in system and stability Theory/Continuous- time H2 Norm

${H_{2}}$-norm of System
The ${H_{2}}$-norm is conceptually identical to the Frobenius (aka Euclidean) norm on a matrix. It can be used to determine whether the system representation can be reduced to its simplest form, thereby allowing its use in performing effective block-diagram algebra.

## The System

Suppose we define the state-space system$G:{L_{2}}\rightarrow {L_{2}}{\text{ by }}y=Gu$ if:
    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)+Du(t)\\\end{aligned}}$
where $A\in \mathbb {R} ^{mxm}$, $B\in \mathbb {R} ^{mxn}$, $C\in \mathbb {R} ^{pxm}$, and $D\in \mathbb {R} ^{qxn}$ for any $t\in \mathbb {R}$. Then the ${H_{2}}$-norm of the system can be determined as described below.

## The Data

In order to determine the ${H_{2}}$-norm of the system, we need the matrices ${A}$, ${B}$, and ${C}$.

## The Optimization Problem

Suppose we wanted to to infer properties of the system behaviour (which is represented in the form (A,B,C,D)). Then it becomes necessary to ensure that the overall system forms an algebra, as the standard use of block-diagram algebra would otherwise be invalid. The only way this is possible is by calculating ${H_{2}}$ and/or ${H_{\infty }}$-norms - both of which are signal norms that (in a certain sense) measure the size of the transfer function.

## The LMI: The $H_{2}$ Norm

Assuming that ${\hat {P}}(s)=C(sI-A)^{-1}B$, this means that the following are equivalent:
       $1)\quad A{\text{ is Hurwitz and }}||{\hat {P}}||_{H_{2}}^{2}<\gamma$
       $2){\begin{aligned}{\begin{cases}trace(CXC^{T})&<\gamma \\AX+XA^{T}+BB^{T}&<0\\X&>0\end{cases}}\end{aligned}}$

## Conclusion:

The LMI can be used to minimize the ${H_{2}}$-norm of the system. It is worth noting that a finite ${H_{2}}$-norm does not guarantee finite ${H_{\infty }}$-norm, and that in order for the block diagram algebra to be valid, ${H_{\infty }}$-norm must be finite.

## Implementation

* Example Code - A GitHub link that contains code (titled "H2Norm.m") that demonstrates how this LMI can be implemented using MATLAB-YALMIP.

## Related LMIs

      * $H_{2}$-Filtering - LMI for $H_{2}$-Filtering
      * Discrete-Time $H_{2}$ Norm - LMI for $H_{2}$-norm in the Discrete-Time case.

## 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.