OpenLLM-France/wikimedia huggingface dataset:
# LMIs in Control/Click here to continue/Controller synthesis/Robust H2 State Feedback Control
## Robust $H_{2}$ State Feedback Control

For the uncertain linear system given below, and a scalar $\gamma >0$. The goal is to design a state feedback control $u(t)$ in the form of $u(t)=Kx(t)$ such that the closed-loop system is asymptotically stable and satisfies.
    ${\begin{aligned}||G_{zw}(s)||_{2}<\gamma \end{aligned}}$

## The System

Consider System with following state-space representation.
    ${\begin{aligned}{\dot {x}}(t)&=(A+\Delta {A})x(t)+(B_{1}+\Delta {B_{1}})u(t)+B_{2}w(t)\\z(t)&=Cx(t)+D_{1}u(t)+D_{2}w(t)\\\end{aligned}}$
where $x\in \mathbb {R} ^{n}$ , $u\in \mathbb {R} ^{r}$ , $w\in \mathbb {R} ^{p}$, $z\in \mathbb {R} ^{m}$. For $H_{2}$ state feedback control $D_{2}=0$
$\Delta {A}$ and $\Delta {B_{1}}$ are real valued matrix functions that represent the time varying parameter uncertainties and of the form
    ${\begin{aligned}{\begin{bmatrix}\Delta {A}&\Delta {B_{1}}\end{bmatrix}}=HF{\begin{bmatrix}E_{1}&E_{2}\end{bmatrix}}\end{aligned}}$
where matrices $E_{1},E_{2}$ and $H$ are some known matrices of appropriate dimensions, while $F$ is a matrix which contains the uncertain parameters and satisfies.
    ${\begin{aligned}F^{T}F\leq I\end{aligned}}$
For the perturbation, we obviously have
    ${\begin{aligned}{\begin{bmatrix}\Delta {A}&\Delta {B_{1}}\end{bmatrix}}={\begin{bmatrix}0&0\end{bmatrix}}\end{aligned}}$, for $F=0$
    ${\begin{aligned}{\begin{bmatrix}\Delta {A}&\Delta {B_{1}}\end{bmatrix}}=H{\begin{bmatrix}E_{1}&E_{2}\end{bmatrix}}\end{aligned}}$, for $F=0$

## The Problem Formulation:

The $H_{2}$ state feedback control problem has a solution if and only if there exist a scalar $\beta$, a matrix $W$, two symmetric matrices $Z$ and $X$ satisfying the following LMI's problem.

## The LMI:

$\min \gamma ^{2}::$
    ${\begin{aligned}{\begin{bmatrix}\langle AX+B_{1}W\rangle _{s}+B_{2}B_{2}^{T}+\beta {H}H^{T)&(E_{1}X+E_{2}W)^{T}\\E_{1}X+E_{2}W&-\beta {I}\end{bmatrix}}<0\end{aligned}}$
    ${\begin{aligned}{\begin{bmatrix}-Z&CX+D_{1}W\\(CX+D_{1}W)^{T}&-X\end{bmatrix}}<0\end{aligned}}$
    ${\begin{aligned}trace(Z)<\gamma ^{2}\end{aligned}}$
where $\langle M\rangle _{s}=(M+M^{T})$ is the definition that is need for the above LMI.

## Conclusion:

In this case, an $H_{2}$ state feedback control law is given by $u(t)=WX^{-1}x(t)$.

## External Links

* LMIs in Control Systems Analysis, Design and Applications - Duan and Yu
* A course on LMIs in Control by Matthew Peet.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
# LMIs in Control/Click here to continue/Controller synthesis/Stabilizability LMI

Stabilizability LMI
A system is stabilizable if all unstable modes of the system are controllable. This implies that if the system is controllable, it will also be stabilizable. Thus, stabilizability is a essentially a weaker version of the controllability condition. The LMI condition for stabilizability of pair $(A,B)$ is shown below.

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t),\\x(0)&=x_{0},\end{aligned}}$
where $x(t)\in \mathbb {R} ^{n}$, $u(t)\in \mathbb {R} ^{m}$, at any $t\in \mathbb {R}$.

## The Data

The matrices necessary for this LMI are $A$ and $B$. There is no restriction on the stability of A.

## The LMI: Stabilizability LMI

$(A,B)$ is stabilizable if and only if there exists $X>0$ such that
       $AX+XA^{T}+BB^{T}<<0$,
where the stabilizing controller is given by
       $u(t)=-{\frac {1}{2}}B^{T}X^{-1}x(t)$.

## Conclusion:

If we are able to find $X>0$ such that the above LMI holds it means the matrix pair $(A,B)$ is stabilizable. In words, a system pair $(A,B)$ is stabilizable if for any initial state $x(0)=x_{0}$ an appropriate input $u(t)$ can be found so that the state $x(t)$ asymptotically approaches the origin. Stabilizability is a weaker condition than controllability in that we only need to approach $x(t)=0$ as $t\rightarrow \infty$ whereas controllability requires that the state must reach the origin in a finite time.

## Implementation

This implementation requires Yalmip and Sedumi.
https://github.com/eoskowro/LMI/blob/master/Stabilizability_LMI.m

## Related LMIs

Hurwitz Stability LMI
Detectability LMI
Controllability Grammian LMI
Observability Grammian LMI

## 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.
* LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013, Section 6.1.1 and Table 6.1 pp. 166–170, 192.
* A Course in Robust Control Theory: a Convex Approach, - by Geir E. Dullerud and Fernando G. Paganini, Springer, 2011, Section 2.2.3, pp. 71-73.
# LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs

Fundamentals of Matrix and LMIs
Fundamentals of Matrix and LMIs
* Basic Matrix Theory
* Notion of Matrix Positivity
* Matrix Inequalities and LMIs
* Convexity of LMIs
* Concatenation of LMIs
Properties of LMIs
* Change of Subject
* Congruence Transformation
* /Young’s Relation (Completion of the Squares)/
** Young’s Relation-Based Properties
** Special Cases of Young’s Relation
** Iterative Convex Overbounding
* Projection Lemma (Matrix Elimination Lemma)
** Strict Projection Lemma
** /Non Strict Projection Lemma/
** Reciprocal Projection Lemma
** Projection Lemma-Based Properties
* Ellipsoidal inequality
* Continuous Time Properties
** Schur Complement
*** Strict Schur Complement
*** Non-Strict Schur Complement
*** Schur Complement Lemma-Based Properties
** Eigenvalue related Problems
*** Matrix Eigen Value Minimization
*** Continuous Time/Eigenvalue Problem
*** LMI for Generalized eigenvalue problem
** Matrix Norm Minimization
** LMI for Generalized Eigenvalue Problem
** LMI for Linear Programming
** LMI for Feasibility Problem
** Continuous Time/Structured Singular Value
** LMI for Minimizing Condition Number of Positive Definite Matrix
** Continuous time quadratic stability
** Minimizing Norm by Scaling
* Discrete Time Properties
** Discrete Time Minimum Gain Lemma
** Discrete Time Modified Minimum Gain Lemma
* Finsler’s Lemma
* Dilation
* Tangential Nevanlinna Pick
* Nevanlinna Pick Interpolation with Scaling
* Deduced LMI Conditions for Hinf Index
* Deduced LMI Conditions for H2 Index
* Dissipativity of Systems
* Generalized H2 Norm
* Passivity and Positive Realness
* Non-Expansivity and boundedness Realness
* Variable Reduction Lemma
* D-stability Rise Poles
* D-stability Settling time poles
* D-stability Max Percent Overshoot Poles
* Iterative Convex Overbounding
* Frobenius Norm
* Dualization Lemma
* Submatrix Determinants and Imaginary and Real Parts
# LMIs in Control/Click here to continue/Controller synthesis/Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

LMIs in Control/Click here to continue/Controller synthesis/Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty
If the system is quadratically stable, then there exists some $\mu \geq 0,P>0,$ and $Z$ such that the LMI is feasible. The $Z$ and $P$ matrices can also be used to create a quadratically stabilizing controller.

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t)+Mp(t),&&p(t)=\Delta (t)q(t),\\q(t)&=Nx(t)+Qp(t)+D_{12}u(t),&&\Delta \in \mathbf {\Delta } \;:=\{\Delta \in \mathbb {R} ^{n\times n}:\|\Delta \|\leq 1\}\\\end{aligned}}$

## The Data

The matrices $A,B,M,N,Q,D_{12}$.

## The LMI:

       ${\begin{aligned}{\text{Find}}\;&P>0,\mu \geq 0,{\text{ and }}Z:\\{\begin{bmatrix}AP+BZ+PA^{T}+Z^{T}B^{T}&PN^{T}+Z^{T}D_{12}^{T}\\NP+D_{12}Z&0\end{bmatrix}}+\mu {\begin{bmatrix}MM^{T}&MQ^{T}\\QM^{T}&QQ^{T}-I\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

There exists a controller for the system with $u(t)=Kx(t)$ where $K=ZP^{-1}$ is the quadratically stabilizing controller, if the above LMI is feasible.

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

H-infinity Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty
Stabilizing State-Feedback Controllers with Structured Norm-Bounded Uncertainty
Optimal State-Feedback Controllers with Structured Norm-Bounded Uncertainty

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
# History of Western Theatre: 17th Century to Now/Canadian 21st

Canadian theatre of the 21st century is reprented by Judith Thompson with "Habitat" (2001).
# History of video games/Platforms/Tassei Denki Project Nadeshiko
## History

The system was shown at Tokyo Game Show 2023, and was not meant to be a production model.

## Gallery

* At Tokyo Game Show 2023.
* At Tokyo Game Show 2023.
* At Tokyo Game Show 2023.

## References

* ↑ Wallace, Anthony (22 September 2023). "Tassei Denki "Project Nadeshiko" Is A New Nintendo DS Clone Straight Out Of Japan". Retro Dodo. https://retrododo.com/project-nadeshiko/.
* ↑ Reynolds, Ollie (22 September 2023). "Random: AMOLED 3DS Concept Shown Off At Tokyo Game Show 2023". Nintendo Life. https://www.nintendolife.com/news/2023/09/random-amoled-3ds-concept-shown-off-at-tokyo-game-show-2023.
# History of video games/Platforms/Technology Will Save Us DIY Gamer Kit
## History
### Legacy

A kit was preserved in the Museum of Modern Art (MoMA).

## References

* ↑ https://www.moma.org/collection/works/184278
# History of video games/Platforms/Telejogo II
## History

The Telejogo II was released in 1978.

## Technology

A General Instrument AY-3-8610 is used by the console.

## References

* 1 2 "Telejogo II for Dedicated console (1978)". MobyGames. Retrieved 11 September 2021.
# History of video games/Platforms/Tandy Video Information System
## History
### Launch

The Tandy Video Information System (VIS) was released in Fall of 1992, and was sold at RadioShack under the Tandy brand at a cost of $699. The system was intended to compete with other home entertainment devices such as the CD-i and the Commodore CDTV. However the system was uncompetitive, and among sales staff, the VIS had the nickname "Virtually Impossible to Sell".

### Legacy

The Tandy Video Information System was discontinued in Spring of 1994 after a price cut to $399, a drastic move which pushed the price $45 below the cost to manufacture the system, failed increase sales. Remaining units were liquidated. This amount of time on the market was rather short, and the desperate measures taken to increase sales demonstrates the difficulties the system found on the market.
The VIS ultimately lost Tandy between 50 and 75 million dollars. About 11,000 systems were likely sold, which was a paltry number for any console, and was especially bad for Tandy given compared to the massive resources they invested in the system.

## Technology

The system was effectively built on a PC architecture, and was among the first gaming devices to run a locked down version of Windows as an operating system.
The Tandy Video Information System uses an 16 bit Intel 80286 CPU clocked at 12.5 megahertz. The system has 1 megabyte of RAM.
Software was based on Modular Windows, a modified version of Windows 3.1. Some software for Modular Windows did not run correctly on the VIS.

## Notable games

Over 60 titles were released for the VIS, most of which were edutainment software.

## Gallery

* VIS logotype.
* Modular Windows Logotype.

## External Resources

* Video Game Kraken - VIS page with detailed history, photo, and software list.

## References

* ↑ "Game Systems". www.lib.umich.edu. Retrieved 30 October 2020.
* 1 2 3 4 5 6 7 8 "Tech Throwback: The Tandy Video Information System". Engadget. Retrieved 30 October 2020.
* 1 2 "Radio Shack Lore Ira Goldklang's TRS-80 Revived Site". Retrieved 30 October 2020.
* 1 2 "Windows 3.1 Obscurities: Tandy's Greatest Flop, Commodore's Zombie". Tedium: The Dull Side of the Internet. Retrieved 30 October 2020.
* ↑ "Tandy Video Information System". Wikipedia. 23 October 2020. Retrieved 15 November 2020.
* ↑ "Home Page". Video Game Console Library. Retrieved 30 October 2020.
* ↑ "Visual Information System (VIS) Debug Card – The Video Game Kraken". Retrieved 27 November 2020.
# History of video games/Platforms/Telescore 750
## History

The Telescore 750 was released in 1977 by French company SEB. The console cost 100 franc in France, the only region it was released.

## Technology

The system uses the Texas Instruments TMS-1965-NC.

## Games

* Tennis

## References

* 1 2 "OLD-COMPUTERS.COM : The Museum". www.old-computers.com. Retrieved 11 September 2021.
* ↑ "Telescore 750". Google Arts & Culture. Retrieved 11 September 2021.
* ↑ "Telescore 750 for Dedicated console (1977)". MobyGames. Retrieved 11 September 2021.
# History of video games/Platforms/Tassei Denki Saturn
## History

The system was shown at Tokyo Game Show 2023 without the intention of retail production.

## Technology

The system used an FPGA to provide compatibility with Sega Saturn games.

## References

* ↑ McFerran, Damien (22 September 2023). "Sega Saturn Mini Could Become A Reality, Thanks To Retron FPGA". Time Extension. https://www.timeextension.com/news/2023/09/sega-saturn-mini-could-become-a-reality-thanks-to-retron-fpga.
* ↑ McDougall, Frank (22 September 2023). "A Glimpse into the Future? Tassei Denki's Concept for a New Nintendo 3DS". Game Is Hard. https://gameishard.gg/news/a-glimpse-into-the-future-tassei-denkis-concept-for-a-new-nintendo-3ds/215953/.
# History of video games/Platforms/Teachermate
## History

The Teachermate was launched on March 13, 2008 in Chicago for $50.

## Technology

The system used an ARM9 architecture 32-bit processor clocked at 200 megahertz.

## References

* 1 2 Yamamoto, Mike (March 13, 2008). "Kindergartners get 'Teachermate' handhelds" (in en). CNET. https://www.cnet.com/culture/kindergartners-get-teachermate-handhelds/.
* ↑ Schaffhauser, Dian. "Stanford, IFL Introducing $50 Handheld to Mexico Students -". THE Journal. https://thejournal.com/articles/2008/07/07/stanford-ifl-introducing-50-handheld-to-mexico-students.aspx.
# History of video games/Platforms/Telejogo
## History

The Telejogo was a Brazilian console, launched on August 2nd, 1977. It was manufactured by Philco, a subsidiary of Ford at the time.

## Technology

The system was based on the National Semiconductor MM57100N.

## Games

* Futebol
* Paredão
* Tennis

## References

* 1 2 3 4 5 "Telejogo Philco Ford - Museu do Videogame Itinerante". web.archive.org. 27 October 2015. Retrieved 11 September 2021.
* ↑ Manikas, Pantelis. "Philco - Ford Telejogo". The voice of the gaming community. Retrieved 28 December 2021.
* ↑ "Tentando ressuscitar a Placa do Telejogo Philco Ford,o primeiro console no Brasil 1° parte". Retrieved 28 December 2021.
# Indian Tipi/Sioux Tipi Pattern

While the general plan of the traditional Indian tipi represents an excellent design as far as smoke exhaustion and the maximum utilization of space are concerned, there are serious limits to its portability. The necessity of providing from 18 to 24 long poles at each site, or of transporting existing poles from site to site, makes the traditional tipi construction suited for the most popular kinds of camping.
# Indian Tipi/Smoke Flaps

Preferably, the structure is erected in such an orientation that the prevailing wind tends to blow toward the back of the tipi. In this manner, the smoke flaps define an opening which is generally downwind, and this improves the draught in the interior of the tipi, so that smoke from a fire built on the ground within the tipi will be drawn up to the peak, and out through the flue opening between the smoke flaps.
It is not essential that the smoke flaps be an exact shape, since their configuration is a matter of choice. The lower corners of the smoke flaps need not be provided, for example, and the flaps can merely be triangular with the vertical edge extending directly from the pocket to the bottom of the flue opening. Where the corners are provided, however, they can be tied out to a tie-pole by cords, thus preventing the smoke flaps from flapping.
# Indian Tipi/Modern Tipi Design

Modern tipis provide a tent structure essentially cone-shaped, including a flue opening in one side adjacent the peak. Two flexible smoke flaps are aligned vertically along the lateral edges of the flue opening. Two truss poles extend from the ground on opposite sides of the tent to a location above the peak, and the peak of the tent is slung from the point where the truss poles meet. Two flap poles extend upwardly from the ground on the side opposite the flue opening, each flap pole crossing one of the truss poles externally and being attached to one of the smoke flaps, in order to maintain the flaps taut in a desired orientation.
# Indian Mythology/Scriptures/Veda

There are total four Vedas.
* Atharva-veda
* Sama-veda
* Yajur-veda
* Rig-veda
Vedas are supposed to be a divine creation. They are the words of Gods. They deal with the various subjects i.e Worship, Mantra, Hums, Philosophy, Music and chanting during rituals.
# Indian Tipi

The tipi was durable, provided warmth and comfort in winter, was dry during heavy rains, and was cool in the heat of summer. Tipis could be disassembled and packed away quickly when a tribe decided to move, and could be reconstructed quickly when the tribe settled in a new area. This portability is important to those who have a nomadic lifestyle.

## Contents

* Title Page
* Tipi History
* Sioux Tipi
** Sioux Tipi Pattern
** Smoke Flaps
** Erecting the Sioux Tipi
** Eighteen Pole Tipi
** Sioux Tipi Parts
** Tipi Doors
** Tipi Lining and Ozan
** Sioux Buffalo Hide Tipi
* Simple Tipi Design
* Modern Tipi Design
* Unusual Tipi Design
* Pole Rack
* Camp Circles
# Indian Tipi/Sioux Tipi

Tents in which open fires can be lit for warmth have been known for hundreds of years. On the North American continent, the Plains Indians have developed different variations of the essentially conical style of tent, generally known as the tipi. The Indian tipi usually has a substantially circular base, and its height from base to apex is about the same as the base diameter. The traditional construction of an Indian tipi involves first erecting a plurality of poles with their lower ends spaced around a circle intended to define the base of the eventual tipi and their upper ends fastened together at the peak. Primarily, the tipi was a conical tent covered with dressed buffalo skins. Everywhere the tipi was made, cared for, and set up by the women. First, a conical framework of long slender poles was erected and the cover raised into place. Then the edges of the cover were staked down and the poles supporting the "ears" put in place. The "ears" are wings, or flies, to keep the wind out of the smoke hole at the top; they were moved about by the outside poles. The fire was built near the center and the beds spread upon the ground around the sides. The head of the family usually sat near the rear, or facing the door.
The "skin" of the tipi, when laid flat on the ground, is generally semi-circular in shape, and includes two smoke flaps extending from the middle area of the side corresponding to the diameter of the semicircle. These smoke flaps, when the tent is wrapped around the erected poles, take up a position in which they extend downwardly from the tipi peak on either side of an opening through which smoke is evacuated from the interior of the tipi. In the traditional construction of the tipi, the smoke flaps are held in a taut condition by flap poles of which the top ends engage the smoke flaps and the bottom ends are dug into the ground. The flap poles bear inwardly against the side of the tent, and are resisted by the support poles inside the tipi.
The entrance to the tipi is directly beneath the smoke flap, and the tipi is always erected so that the entrance and the smoke hole are directed away from the prevailing wind. In order to achieve a good draught so that the smoke from the interior fire will exit through the smoke hole, the traditional tipi is at least 12 feet high, and often as much as 18 or 20 feet in height.
# Indian Mythology/Scriptures/Epics

The two most important epics in the Indian mythology are Mahabharatha and Ramayana.
Each tells the story of one of the lord Vishnu's 24 incarnations on earth. The narration and the characters as depicted in the Ramayana portray the model code of conduct, a conduct which is free of guilt. Lord Ram is the Maryadapurusottam; the most ideal human being on earth his conduct is free of fault of any kind. Ramayana is an ideal world. Mahabharata on the other hand is a narration on the statehood and state policy. Mahabharata's is a real world full of deception, intrigue, cruelty and ambition. It is real war between Dharma (the one which could be born) and Adharma (the one which is not worth being born). The emotions are real. It is a treatise on politics and national policy.
# Metabolomics/Applications/Nutrition/Personal Metabolomics/Genotypes

Back to Previous Chapter: Databases Next chapter: Contributors
First Category: Disease Research Next Section: Lifestyle Go to: Phenotypes

## Web Resources

Effect of genotype on success of lifestyle intervention in subjects at risk for type 2 diabetes
# Metabolomics/Hormones

Back to Previous Chapter: Metabolites Next chapter: Analytical Methods

# Hormones

Hormones are defined as chemical signals that affect one or more cells in an organism. Hormones can have an amplification effect where a small signal causes a large response.

## Table of Contents

* Insulin
* Glucagon
* Somatostatin
* Corticosteroids
* Mineralocorticoids
* Leptin
* Adiponectin
* Ghrelin
# Metabolomics/Applications/Nutrition/Personal Metabolomics/Phenotypes

Back to Previous Chapter: Databases Next chapter: Contributors
First Category: Disease Research Next Section: Lifestyle Go to: Genotypes
# Metabolomics/Contributors

Back to Previous Chapter: Applications Go to First Chapter: Introduction to Metabolomics
* Tung Luong Guiltyblade (talk)
* Katie Grimshaw
* Sophia Lafergola DieselSandwich (talk)
* Kevin King
* Lindsay Littman