OpenLLM-France/wikimedia huggingface dataset:
# LMIs in Control/Applications/F16 Longitudinal Stabilitzation

F-16 Longitudinal Stabilization using Hinf Output Feedback
The linearized longitudinal dynamics of the F-16 aircraft are considered in this example. The nonlinear 6DOF model is linearized using straight-and-level flight conditions of:
${\begin{aligned}V=502ft/s\\{\bar {q}}=300psf\\X_{cg}=0.35{\bar {c}}\\\delta _{trim}=-0.7588deg\end{aligned}}$
See chapter 3 of for further details.

## The System

The state-space representation for the linearized longitudinal dynamics can be written as follows:
${\begin{aligned}{\dot {x}}(t)&=Ax(t)+B_{1}w(t)+B_{2}u(t)\\y(t)&=C_{1}x(t)+D_{11}w(t)+D_{12}u(t)\\z(t)&=C_{2}x(t)+D_{21}w(t)+D_{22}u(t)\\u(t)=Ky(t)\\\end{aligned}}$
where $x=[V\quad \alpha \quad \theta \quad q]^{\text{T}}$, $u=\delta$ , $w=\delta _{cmd}$, and $z=[a_{n}\quad (\delta _{cmd}-\delta )]^{\text{T}}$ are the state variable, control input, disturbance, and regulated output vectors, respectively. In this case, $V$ is velocity (ft/s), $\alpha$ is angle of attack (rad), $\theta$ is pitch (rad), $q$ is pitch rate (rad/s), $\delta$ is elevator deflection with respect to trimmed deflection (rad), $\delta _{cmd}$ is commanded elevator deflection with respect to trimmed deflection (rad), and $a_{n}$ is normal acceleration at the pilot location (ft/s^2).

## The Data

For the linearization used, the above matrices are:
${\begin{aligned}A={\begin{bmatrix}-1.9311e-2&&8.8157&&-3.217e1&&-5.7499e-1\\-2.5389e-4&&-1.0189&&0&&9.0506e-1\\0&&0&&0&&1\\2.9465e-12&&8.2225e-1&&0&&-1.0774\end{bmatrix}}\end{aligned}}$
$B_{1}={\begin{bmatrix}1.737e-1\\-2.1499e-3\\0\\-1.7555e-1\end{bmatrix}}$
$B_{2}={\begin{bmatrix}1.737e-1\\-2.1499e-3\\0\\-1.7555e-1\end{bmatrix}}$
${\begin{aligned}C_{1}={\begin{bmatrix}0&&5.729578e1&&0&&0\\0&&0&&0&&5.729578e1\end{bmatrix}}\end{aligned}}$
${\begin{aligned}C_{2}={\begin{bmatrix}0.003981&&15.88&&0&&1.481\\0&&0&&0&&0\\\end{bmatrix}}\end{aligned}}$
$D_{11}=D_{12}=0$
$D_{21}={\begin{bmatrix}0\\1\end{bmatrix}}$
$D_{21}={\begin{bmatrix}0.03333\\-1\end{bmatrix}}$

## The LMI: Optimal Output Feedback $H_{\infty }$ Control LMI

The following are equivalent.
1) There exists a ${\hat {K}}={\begin{bmatrix}A_{K}&B_{K}\\C_{K}&D_{K}\end{bmatrix}}$ such that $||S(K,P)||_{H_{\infty }}<\gamma$
2) There exists $X_{1}$, $Y_{1}$, $Z$, $A_{n}$, $B_{n}$, $C_{n}$, $D_{n}$ such that
       ${\begin{bmatrix}X_{1}&I\\I&Y_{1}\end{bmatrix}}>0$
       ${\begin{bmatrix}AY_{1}+Y_{1}A^{\text{T}}+B_{2}C_{n}+C_{n}B_{2}^{\text{T}}&*^{\text{T}}&*^{\text{T}}&*^{\text{T}}\\A^{\text{T}}+A_{n}+(B_{2}D_{n}C_{2})^{\text{T}}&X_{1}A+A^{\text{T}}+B_{n}C_{2}+C_{2}^{\text{T}}B_{n}^{\text{T}}&*^{\text{T}}&*^{\text{T}}\\(B_{1}+B_{2}D_{n}D_{21})^{\text{T}}&(X_{1}B_{1}+B_{n}D_{21})^{\text{T}}&-\gamma I&*^{\text{T}}\\C_{1}Y_{1}+D_{12}C_{n}&C_{1}+D_{12}D_{n}C_{2}&D_{11}+D_{12}D_{n}D_{21}&-\gamma I\\\end{bmatrix}}<0$

## Conclusion:

Using this problem formulation, an output controller ${\hat {K}}$ can be found that attenuates normal acceleration and tracks reference elevator deflection command.

## References

Stevens, Brian L., et al. Aircraft Control and Simulation. Third ed., Wiley, 2016.
# LMIs in Control/Applications/An LMI for Multi-Robot Systems

An LMI for Multi-Robot Systems
      * Consensus for Multi-Agent Systems
# LMIs in Control/Applications

      * LMI for Attitude Control of Nonrotating Missiles, Pitch Channel
      * LMI for Attitude Control of Nonrotating Missiles, Yaw/Roll Channel
      * LMI for H2/Hinf Polytopic Controller for Robot Arm on a Quadrotor
      * An LMI for the Kalman Filter
      * Hinf Optimal Model Reduction
      * An LMI for Multi-Robot Systems
      * Helicopter Inner Loop LMI
      * Hinf LMI Satellite Attitude Control
      * H2 LMI Satellite Attitude Control
      * Mixed H2-H∞ LMI Satellite Attitude Control
      * Mixed H2/Hinf LMI Satellite Attitude Control
      * Problem of Space Rendezvous and LMI Approaches
      * LMI for Attitude Control of BTT Missiles, Roll Channel
      * LMI for Attitude Control of BTT Missiles, Pitch/Yaw Channel
# Materials Science/Materials
## Materials

Materials are physical substances used as inputs to production or manufacturing. Raw materials are first extracted or harvested from the earth and divided into a form that can be easily transported and stored, then processed to produce "semi-finished materials". These can be input into a new cycle of production and "finishing processes to create "finished materials", ready for distribution and consumption.
An example of a raw material is cotton, which can be processed into thread, and then processed into cloth, a semi-finished material. Sewing and cutting the fabric turns it into a garment, which is a finished material. Steelmaking is another example—raw materials are extracted, refined and processed into steel, a semi-finished material. Steel is then used as an input in many other industries to make finished products.
* Composite Materials
* Concrete
* Semiconducters
* Metals
* Liquid Crystals
* Ceramics
* Polymers

## Partial Comparison of Materials

| Type | Bonding | Properties | Thermal/electrical conductivity | optical |
| Metals | Metallic | | high | opaque, reflective |
| Polymers | Secondary | soft, ductile, low strength | insulators | translucent/ transparent |
| Ceramics | Mostly Ionic | brittle, glassy, elastic | Insulators | |
| Semiconductors | covalent | ?? | Between conductors and insulators | |
# Materials Science/Biocompatible Material
## Biocompatible material

In surgery, a biocompatible material (sometimes shortened to biomaterial) is a synthetic or natural material used to replace part of a living system or to function in intimate contact with living tissue. Biocompatible materials are intended to interface with biological systems to evaluate, treat, augment or replace any tissue, organ or function of the body. Biomaterials are usually non-viable, but may also be viable.
A biocompatible material is different from a biological material such as bone that is produced by a biological system. Artificial hips, vascular stents, artificial pacemakers, and catheters are all made from different biomaterials and comprise different medical devices.
Biomimetic materials are not made by living organisms but have compositions and properties similar to those made by living organisms. The calcium hydroxylapatite coating found on many artificial hips is used as a bone replacement that allows for easier attachment of the implant to the living bone.
Surface functionalization may provide a way to transform a bio-inert material into a biomimetic or even bio-active material by coupling of protein layers to the surface, or coating the surface with self-assembling peptide scaffolds to lend bioactivity and/or cell attachment 3-D matrix.
Different approaches to functionalization of biomaterials exist. Plasma processing has been successfully applied to chemically inert materials like polymers or silicon to graft various functional groups to the surface of the implant. Polyanhydrides are polymers successfully used as a drug delivery materials.
# How to use a Motorola DVR/Using Tivo

* How to use a Motorola DVR Identify | Connections | Setup | i-Guide | MSTV | Passport | Tivo | FireWire | Remote | Firmware/Software | Configuration | Bugs | Boot Errors | VOD Errors | Resets | Help
This page (and probably subpages) will contain general information on using the DVR (using the tuners, setting up and playing recordings, etc..) for those programmed with Tivo software.
Comcast began rolling out Tivo software, currently only in the Boston area, as an extra-cost option in December 2007. There is a $2.95/month extra charge, on top of the normal DVR fee. The software change requires a technician visit to monitor the upgrade, as there are issues with proper signal levels that must be confirmed first. The Tivo software uses the faster DOCSIS modem for communication instead of the OOB tuner.
As always, do NOT simply copy text or images from a manual! That is a copyright violation!!
Initial Software Version
Motorola Firmware Version 16.43 - Platform Built Sept 25, 2007
Middleware Version: 5.8.09
TiVo Software Version: TE-1.0.2-0021-01-01-001
Software Versions
TiVo Software Version: TE 1.0.3-0078-01-01-001
Middleware Version: 7.8.26
Reported Fixes: Dolby Digital on DCH style boxes. HD channel filtering bug, Suggestions not clearing on their own, single show recording issues, various background fixes
New Bugs: Slow recording scheduling, slow user interface
TiVo Software Version: TE 1.0.5-0085-01-01-001
Middleware Version: 7.8.26
Latest Software Version
TiVo Software Version: TE 1.0.5.2-0003-01-01-001
Middleware Version: 2.2.17

## Enable 30-second skip

Go to your TiVo Recordings list and play back a recording.
Enter the following key sequence on the remote control: Rewind, Slow, Fast Forward, Play, 3, 0, Advance
(The Advance key (aka skip-to-tick key) is the key that looks like ( ->| ) .) (Doesn't work on Tivo HD)
The user will hear 3 chime sounds to indicate that the 30-second skip backdoor has been successfully enabled. The user can enter the same key sequence again to turn off the 30-sec skip backdoor.
With the 30-sec skip backdoor enabled, and while in "Play" mode in Live TV, a recording, or an ON DEMAND program, pressing the Advance key ( ->| ) will jump ahead 30 seconds. While in "Fast Forward" or "Rewind" mode, pressing the Advance key will jump to the next tick mark on the trickplay bar.
If the set-top box is restarted, the 30-sec skip backdoor setting is not maintained. Following a restart, the user will need to enter the backdoor key sequence again to re-enable the 30-sec backdoor.

## External Links

* Comcast Tivo Preview from Gizmodo
* Comcast's official page about the Tivo rollout
# How to use a Motorola DVR/Using i-Guide

* How to use a Motorola DVR Identify | Connections | Setup | i-Guide | MSTV | Passport | Tivo | FireWire | Remote | Firmware/Software | Configuration | Bugs | Boot Errors | VOD Errors | Resets | Help

## Major Sections

* The Basics - Basic operation of the DVR
* User Setup - How to customize i-Guide features
* Parental Control - How to use the Parental Control features
* Recording - How to use the recording features
# How to use a Motorola DVR/Identifying your model
## Identifying which model Motorola DVR you have

There are 3 known versions of the DCT64xx, named Phase I, Phase II, and Phase III.
* Phase I is identified by the model number DCT-6412/2000 on a label on the bottom of the unit.
* Phase II is identified by the model number DCT-6412/2005, and has the Comcast logo.
* Both Phase I and Phase II have only a single RF input connector on the back. There is no RF output connector.
* Phase III is identified by:
** The 6412 III logo on the front of the unit.
** An HDMI port on the back of the unit instead of the DVI port on older versions.
** A SATA port on the back of the unit.
** (optional) An RF output jack on the back of the unit.
Little is known about the differences between the Phase I and Phase II.
Beyond the external differences, the Phase III has better analog picture quality and the 12.xx firmware revision (the older models use 9.xx). As of September 2006, the firmware for DCT-34xx and DCT-64xx Phase I, II & III boxes has converged on 16.xx version numbers.
The Motorola 34xx is similar to the Phase III 64xx, but has no analog tuner and can only be used on cable systems where analog-digital simulcasting (ADS) is set up.
The 34xx is about the same width and height as the 64xx, but is not as deep (about 11 inches, versus 13 inches on the 64xx). On the front it has no SmartCard slot, no A/V input, and no USB port (there is still one USB port on the back). On the back, there are no A/V inputs and no metal cover where the RF connectors are.
The DCT3080 is similar to the DCT3412, but has no HD output circuitry. It can record HD, but will only play it back in SD. On the back, it does not have component, FireWire or HDMI ports.
The QIP6416 has A/V inputs on the front, but no SmartCard slot (it has been moved to the back). On the back, there is no SATA port. The QIP6416 has no analog tuner, but includes an IP tuner that uses frequencies from 1.125GHz to 1.425GHz, making it a "hybrid" digital cable box.
The DCT6208 is the same size and generally looks similar to the 6412. It is identified by the model number DCT-6208/2005 on a label on the bottom of the unit.
The DCH3416 has a very different look than the DCT series. It has a large clear/black center, with many of the buttons along the bottom. On the back, it has an M-Card slot for a card that contains encryption security codes.
The DCH6416 is similar to the DCH3416, but also has an analog tuner.

## Pictures

Below are front and rear pictures of the various Motorola DVR's.

### DCT-3080

[Motorola_3080_front] [Motorola_3080_Back] [Motorola_3080_inside]

### QIP-7216

The QIP 7216 is nearly identical to the 6416 except for a M-Card slot on the back, the removal of the composite inputs on the front, and different vent screen pattern, on the top. The QIP 7216 has more RAM, offers MPEG-4 and Dolby Digital 7.1 support.

### DCH-6416

(need pictures) It looks VERY MUCH like the 3416 on the front and back side.
# How to use a Motorola DVR/Online help
### Official Motorola Pages

* Motorola's DVR FAQ for DCT6208/DCT6412
User manual and specs can be accessed from the pages listed below, under "Resources Spotlight".

### HOWTO / Informational Guides

* HowTO record via 1394/Firewire to WindowsXP A guide to transfer recorded or live programs from the STB to a PC
* DCT6412 Firewire capture and HD/SD to DVD guide A more polished guide on transferring programs to a PC, based on the AVS forum thread
* DCT6412 with Passport Echo software (Cox cable markets)

### Online Discussion Forums

Note: A wealth of information is often first reported to the AVS Forums
* Official Comcast 6412 w/ iGuide Discussion at AVS Forums The premier source for information on the 6412
* Washington State - Comcast 6412 w/ MSFT Software at AVS Forums 6412 discussion specific to the MSTV Foundation Edition IPG
* Official Comcast 3412 & 3416 STB Discussion at AVS Forums The premier source for information on the (largely similar) successor models
* www.dvrchatter.com Rich in information, DVRChatter is straight to the point, with no meandering threads.
* Digital Home Canada Digital Home Canada's digital cable forums for Shaw, Rogers Atlantic, and Cogeco offer a great resource of information about the Motorola DVR. Also, a host of other wired home subjects are talked about on this site. The technical information is applicable whether you are Canadian or American.
# How to use a Motorola DVR/Using Microsoft TV Foundation Edition

* How to use a Motorola DVR Identify | Connections | Setup | i-Guide | MSTV | Passport | Tivo | FireWire | Remote | Firmware/Software | Configuration | Bugs | Boot Errors | VOD Errors | Resets | Help
In Washington State, Comcast tried the Microsoft TV: Foundation Edition for several months, but switched to i-Guide in 2007.
No cable companies are currently using MSTV on Motorola DVRs.
# How to use a Motorola DVR/Using Passport Echo

* How to use a Motorola DVR Identify | Connections | Setup | i-Guide | MSTV | Passport | Tivo | FireWire | Remote | Firmware/Software | Configuration | Bugs | Boot Errors | VOD Errors | Resets | Help
This page (and probably subpages) will contain general information on using the DVR (using the tuners, setting up and playing recordings, etc..) for those programmed with Passport Echo.
As always, do NOT simply copy text or images from a manual! That is a copyright violation!!
# General Framework

The general frameworks (GF) are the equivalent to the general learning outcomes of the biological, cognitive, and sociocultural levels of analysis.
There are two general frameworks:
* GF1: To what extent do biological, cognitive and sociocultural factors influence human relationships?
* GF2: Evaluate psychological research (that is, theories and/or studies) relevant to the study of human relationships.
Note that any example responses are not necessarily worth full marks, but exist simply to provide an idea of how an example looks.

# GF1

To what extent do biological, cognitive and sociocultural factors influence human relationships?

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# GF2

Evaluate psychological research (that is, theories and/or studies) relevant to the study of human relationships.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.
# General Framework

The general frameworks (GF) are the equivalent to the general learning outcomes of the biological, cognitive, and sociocultural levels of analysis.
There are two general frameworks:
* GF1: To what extent do biological, cognitive and sociocultural factors influence behaviour in sport?
* GF2: Evaluate psychological research (that is, theories and/or studies) relevant to the study of sport psychology.
Note that any example responses are not necessarily worth full marks, but exist simply to provide an idea of how an example looks.

# GF1

To what extent do biological, cognitive and sociocultural factors influence behaviour in sport?

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# GF2

Evaluate psychological research (that is, theories and/or studies) relevant to the study of sport psychology.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.
# Psychology of Human Relationships

    General Framework
       GF1: To what extent do biological, cognitive and sociocultural factors influence human relationships?
       GF2: Evaluate psychological research (that is, theories and/or studies) relevant to the study of human relationships.
    Social Responsibility
       SR1: Distinguish between altruism and prosocial behaviour.
       SR2: Contrast two theories explaining altruism in humans.
       SR3: Using one or more research studies, explain cross-cultural differences in prosocial behaviour.
       SR4: Examine factors influencing bystanderism.
    Interpersonal Relationships
       IR1: Examine biological, psychological and social origins of attraction.
       IR2: Discuss the role of communication in maintaining relationships.
       IR3: Explain the role that culture plays in the formation and maintenance of relationships.
       IR4: Analyse why relationships may change or end.
    Violence
       V1: Evaluate sociocultural explanations of the origins of violence.
       V2: Discuss the relative effectiveness of two strategies for reducing violence.
       V3: Discuss the effects of short-term and long-term exposure to violence.
# General Framework

The interpersonal relationships (IR) outcomes investigate the close relationships that people form with each other.
There are four interpersonal relationships outcomes:
* IR1: Examine biological, psychological and social origins of attraction.
* IR2: Discuss the role of communication in maintaining relationships.
* IR3: Explain the role that culture plays in the formation and maintenance of relationships.
* IR4: Analyse why relationships may change or end.
Note that any example responses are not necessarily worth full marks, but exist simply to provide an idea of how an example looks.

# IR1

Examine biological, psychological and social origins of attraction.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# IR2

Discuss the role of communication in maintaining relationships.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# IR3

Explain the role that culture plays in the formation and maintenance of relationships.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# IR4

Analyse why relationships may change or end.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.
# General Framework

The social responsibility (SR) outcomes concentrate on behaviour that is considered accepted in society, and that which has come to be expected by individuals, groups, and organisations.
There are four social responsibility outcomes:
* SR1: Distinguish between altruism and prosocial behaviour.
* SR2: Contrast two theories explaining altruism in humans.
* SR3: Using one or more research studies, explain cross-cultural differences in prosocial behaviour.
* SR4: Examine factors influencing bystanderism.
Note that any example responses are not necessarily worth full marks, but exist simply to provide an idea of how an example looks.

# SR1

Distinguish between altruism and prosocial behaviour.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# SR2

Contrast two theories explaining altruism in humans.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# SR3

Using one or more research studies, explain cross-cultural differences in prosocial behaviour.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# SR4

Examine factors influencing bystanderism.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.
# General Framework

The violence (V) outcomes look at the effects of intergroup physical conflicts.
There are three violence responsibility outcomes:
* V1: Evaluate sociocultural explanations of the origins of violence.
* V2: Discuss the relative effectiveness of two strategies for reducing violence.
* V3: Discuss the effects of short-term and long-term exposure to violence.
Note that any example responses are not necessarily worth full marks, but exist simply to provide an idea of how an example looks.

# SR1

Evaluate sociocultural explanations of the origins of violence.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# SR2

Discuss the relative effectiveness of two strategies for reducing violence.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.

# SR3

Discuss the effects of short-term and long-term exposure to violence.

## Example response

There is no example response yet for this outcome.

## Additional Notes

There are no additional notes yet for this outcome.
# Sport Psychology

    General Framework
       GF1: To what extent do biological, cognitive and sociocultural factors influence behaviour in sport?
       GF2: Evaluate psychological research (that is, theories and/or studies) relevant to the study of sport psychology.
    Emotion and Motivation
       EM1: Evaluate theories of motivation in sport.
       EM2: Using one or more research studies, explain the role of goal-setting in the motivation of individuals.
       EM3: Discuss theories relating arousal and anxiety to performance.
    Skill Development and Performance
       SDP1: Evaluate techniques for skill development used in sport.
       SDP2: To what extent does the role of coaches affect individual or team behaviour in sport?
       SDP3: Explain relationships between team cohesion and performance.
       SDP4: Describe aids and barriers to team cohesion.
    Problems in Sports
       PS1: Discuss athlete response to stress and chronic injury.
       PS2: Examine reasons for using drugs in sport.
       PS3: Discuss effects of drug use in sport.
       PS4: Compare models of causes and prevention of burnout.