OpenLLM-France/wikimedia huggingface dataset:
# Handbook of the Swatow Vernacular modernized/A List of Animals and Birds
## Lesson XXVI. a list of animals and birds.

| Pêng'im | TL | Characters | English |
| sai1 | sai | 獅 | Lion, |
| houn2, lao6houn2 | hóunn, lău-hóunn | 虎　老虎 | Tiger, |
| ciên6 | tshiĕnn | 象 | Elephant, |
| sai1ghu5 | sai-gû | 犀牛 | Rhinoceros, |
| loh8toh8 | lóh-thôh | 駱駝 | Camel, |
| le5, lo5 | lûr, lô | 驪　騾 | Ass, |
| dêg8 | têk | 鹿 | Deer, |
| cai5lang5 | tshâi-lâng | 豺狼 | Wolf, |
| hou6lai5 | hŏu-lâi | 狐狸 | Fox, |
| zua5 | tsûa | 蛇 | Snake, |
| gao5 | kâu | 猴 | Monkey, |
| suan1nang5 | suann-nâng | 山人 | Orang-outang, |
| him1 | him | 熊 | Bear, |
| kong2ciêh4 | khóng-tshieh | 孔雀 | Peacock, |
| suan1goi1 | suann-koi | 山雞 | Pheasant, |
| hong6 | hŏng | 鳳 | Phoenix, |
| lêng5 | lêng | 龍 | Dragon, |
| ziou2 | tsióu | 鳥 | Bird, |
| êng1go1 | eng-ko | 鸚哥 | Parrot, |
| êng1bo1 | eng-pô | 鸚婆 | Hawk, |
| hoh8, bêh8liou7si1 | hôh, pêh-liōu-si | 鶴　 白鷺𮈔 | Stork, |
| ziêh8ce2 | tsiêh-tshúr | 石鬣 | Rabbit, |
| muan5ziah4ziou2 | mûann-tsiah-tsióu | | Sparrow, |
| hung2ziou2 | hún-tsióu | 粉鳥 | Pigeon, |
| bhuê2iah8 | búe-iâh | 蝴蝶 | Butterfly, |
| sua1mên1 | sua-menn | 沙𧋎 | Dragon-fly, |
| cao2mên2 | tsháu-ménn | 草蟒 | Grasshopper, |
| pang1 | phang | 蜂 | Bee, |
| zui2ghu5 | tsúi-gû | 水牛 | Buffalo, |
| ghu5 | gû | 牛 | Cow, |
| min2iên5 | mînn-iênn | 麋羊 | Sheep, |
| suan1iên5 | suann-iênn | 山羊 | Goat, |
| bhê2 | bé | 馬 | Horse, |
| de1 | tur | 猪 | Pig, |
| gao2 | káu | 狗 | Dog, |
| ngiou1 | ngiou | 貓 | Cat, |
| ngiou2ce2 | ngióu-tshúr | 貓鬣 | Rat, |
| gê1gang1 | gê-kang | 蜈蚣 | Centipede, |
| zui2goi1 | tsúi-koi | 水雞 | Frog, |
| gab4bo5 | kap-pô | 蛤婆 | Toad, |
| ga1zuah8 | ka-tsuâh | 膠賊 | Cockroach, |
| zin5lêng5 | tsînn-lêng | 蠐龍 | Lizard, |
| bhê2lêng5kia5 | bé-lêng-khiâ | 螳螂 | Spider, large, |
| di1du1 | ti-tu | 蜘蛛 | Spider, little, |
| hou5sing5 | hôu-sîn | 蝴蠅 | Fly, |
| mang2 | máng | 蟒 | Mosquito, |
| bhung1 | bun | 蚊 | Gnat, |
| tang5 | thâng | 虫 | Worm, |
| cêh4he5 | tsheh-hûr | 册魚 | Worm, in books. |
| hia7 | hiā | 蟻 | Ant, |
| ga1zao2 | ka-tsáu | 蝨 | Flea, |
| sag4 | sat | 虱 | Louse, |
# Handbook of epistemology/Learning the mastery of oneself

content transferred in :
Handbook of epistemology/The pedagogy of autonomy
Handbook of epistemology/The therapeutic virtues of autonomy
# Handbook of epistemology/Modeling the knowledgeable body

Parts of this old chapter have been transferred to the first four chapters of the new edition.
# Handbook of epistemology/Silent and talking knowledge

Parts of this old chapter have been transferred to 'Perception and imagination' and 'Speech'
# Lojban/Acronyms

Lojbanic acronyms are formed simply by stringing the names of the lerfu together in a cmene. For example, the acronym BBC (British Broadcasting Corporation) would be written in Lojban as la bybycys. (remember: cmene mustn't end in a vowel!). Also, for vowels, it is not required to write them ending in -bu, all that is requred is that it is obvious that the letter sound is there. So NASA (National Aeronautics and Space Administration) would be written as la ny'asy'as. (or la ny,asy,as., just so long as there are no nonsensical vowel clusters). There are a few quirks here and there, as Lojban is not known for its range of sounds (especially semivowels). Just remember these when transliterating acronyms: h=x, y=j, w=v.
Here are some examples of Lojbanic acronyms:
-CNN (Cable News Network): la cynynys.
-DFTBA (Don't Forget To Be Awesome): la dyfytyby'as.
-NBC (National Broadcasting Company): la nybycys.
-USA (United States of America): la .usy'as. (remember: cmene starting in a vowel must have a <.> in front of them)
-USSR (Union of Soviet Socialist Republics): la .usysyrys.
-USAPATRIOT (Uniting and Strengthening America by Providing Approprate Tools Required to Intercept and Obstruct Terrorism): la .usy'apy'atyry'i'otys.
-GLaDOS (Genetic Life-form and Disk Operating System): la gyly'ady'osys.
-LASER (Light Amplification by Stimulated Emission of Radiation): la ly'asy'erys.
-SCUBA (Self Contained Underwater Breathing Apparatus): la sycy'uby'as
-TASER (Thomas A. Swift's Electric Rifle): la ty'asy'arys.
-ATM (Automatic Teller Machine): la .atymys.
Now try to come up with some of your own acronyms!
# Lojban/Anaphora/Subscription

Anaphora subscription is the process by which one (the narrator) may unambiguously refer a sumti or bridi/selbri by using a cmavo instead (such as a pro-sumti or pro-bridi, respetively), but in some manner other than the default of the pro-sumti/pro-bridi. This method employs Lojban numerals and the entire cmavo-subscript-numeral reference is usually written as one word.

## Additional Notes and/or Examples

* [lo smuci .i lo forca .i la rik. pilno rixire .i la .alis. pilno riximu]
    = A spoon. A fork. Rick uses (ri-sub-two = repeat penultimate = a fork). Alice uses (ri-sub-five = repeat fifth-from-last/second from antepenultimate = a spoon).
* [go'ixire] is the same as [go'e].
* [faxixa] refers to the 6th sumti position of a brivla.
# Lojban/Culturally neutral

Culturally neutral
Lojban attempts to maintain cultural neutrality, particularly as compared to other constructed languages such as Esperanto which use European languages, sounds or conventions as their basis. The main sources of Lojban basic vocabulary are the six most widely spoken languages (at least during Lojban's birth): Mandarin, English, Hindi, Spanish, Russian, and Arabic; the mishmash gives Lojban a truly international flavor and keeps the language's style and sound from favoring one culture over another, as much as feasibly possible.
Lojban words never automatically insinuate the gender of the subject or speaker, contrary to English and other languages: if gender is not stated explicitly in Lojban, it is not implied. Likewise for tense, spatial or temporal are not implied in default Lojban grammar and must be manually added. These too serve to keep Lojban culturally neutral, and to draw attention to gender and tense only when a speaker or writer feels the need to.
Lojban also has a marker (pe'a) to designate figures of speech, thus 'back stabber' translated as-is into Lojban would always be taken literally as 'one who physically stabs physical backs', unless otherwise indicated, in order to set aside, deconstruct and learn from cultural linguistic constructs, all on common ground.
Lojban endeavors to provide a neutral linguistic structure upon which people can build, rather than enforce linguistic sterility. By starting with a system that is as neutral as possible and drawing attention to culturally weighted concepts, Lojban seeks to make ambiguity and culture-specific language visible and clear, rather than remove it.
# Lojban/Cmene

In Lojban names are called cmene (pronouced shmen-eh, IPA /ʃme.ne/), and are transliterated to use only Lojban sounds. In Lojban all words end in a vowel, and so to avoid any possible confusion all cmene end in a consonant; if a transliterated name would end in a vowel, it is usual to add an s to the end. All cmene are followed by a full stop, so confusion to where the name stops and the next word starts it avoided; for this reason, any names beginning in a vowel have a full stop in front of them. To indicate an accent somewhere other than the second-to-last syllable, the entire syllable to be accented must be capitalised. A comma should be used to stop two vowels next to each other that should not be pronouced as a dipthong. All names must have the word 'la', meaning 'the', placed before them. A few examples are below:
| English | Lojban |
| New York | nu,IORK (in some accents ni,IORK) |
| Cynthia | sinti,a (pronounced SEEN-tee-ah) |
| Daniel | daniyl (DAHN-yuhl) |

## Exercises
### English names to Cmene

Translate these names to Lojban cmene.
* Jacob
* Emily
* Michael
* Madison
* Joshua
* Hannah
* Matthew
* Emma
* Ethan
* Alexis
* Joseph
* Ashley
* Andrew
* Abigail
* Christopher
* Sarah
* Daniel
* Samantha
* Nicholas
* Olivia

### Cmene to English names

Translate these Lojban cmene to English names.
* la .ueliem.
* la .ilezabet.
* la .entonis.
* la .alesas.
* la deived.
* la laren.
* la tailer.
* la .ezabelas.
* la .alekzander.
* la greis.
* la rai,en.
* la djeseka.
* la djan.
* la brianas.
* la djeimz.
* la teiler.
* la zekeris.
* la keilas.
* la brendan.
* la .ennas.

## Answers to Exercises

No one pronouciation of a name is the right one, so use common sense whe deciding if you got these right or not.

### English names to Cmene

* la djeikeb.
* la .emelis.
* la maikel.
* la medesen.
* la djaciu,as.
* la xennas.
* la ma'ius.
* la .emas.
* la .i'an.
* la .alekses.
* la djosef.
* la .aclis.
* la .endrus.
* la .ebegeil.
* la krestofer.
* la seiras.
* la daniel.
* la samentas.
* la nekoles.
* la .olevias.

### Cmene to English names

* William
* Elizabeth
* Anthony
* Alyssa
* David
* Lauren
* Tyler
* Isabella
* Alexander
* Grace
* Ryan
* Jessica
* John
* Brianna
* James
* Taylor
* Zachary
* Kayla
* Brandon
* Anna
# Lojban/Bridi

This page is part of a pre-draft textbook. Therefore some information is inaccurate.

## Definition

bridi is the concept of sentences that can be composed by the use of a predicate and several called arguments. It corresponds to the linguistic concept of a clause.
A predicate together with its arguments (called sumti) is a bridi. A bridi's relations are expressed by a brivla.

## Example

The statement mi prenu (I'm a person) is a bridi where x1 prenu is a brivla and mi is the sumti of the brivla.
# Lojban/Dates

There are two systems of naming months in use: one based on the zodiac, and one based on numbers. The place structure is "x1 is foomonth in year x2 in calendar x3"; this is not according to jvojva but makes it easy to specify dates as "the day nth of the foomonth of the year mmmm".
| English name | Zodiac name | Number name |
| January | kanbyma'i | pavma'i |
| February | jaurbeima'i | relma'i |
| March | fipma'i | cibma'i |
| April | lanma'i | vonma'i |
| May | bakma'i | mumyma'i |
| June | matsi'uma'i | xavma'i |
| July | mlajukma'i | zelma'i |
| August | cinfyma'i | bivma'i |
| September | xlima'i | sozma'i |
| October | laxma'i | pavnonma'i |
| November | rebjukma'i | pavypavma'i |
| December | celma'i | pavrelma'i |
There are also systems of naming the days of the week based on Oriental elements and numbers.
| English name | Oriental el. name | Number name |
| Monday | lurdei | pavdei |
| Tuesday | fagdei | reldei |
| Wednesday | jaurdei | cibdei |
| Thursday | mudydei | vondei |
| Friday | jimdei | mumdei |
| Saturday | tedydei | xavdei |
| Sunday | soldei | zeldei or nondei |
Note that Sunday in Lojban is either day seven or day zero, depending on your perspective.
# Lua in SpringRTS/Callins/GameStart
## GameStart
### Description

Gets run once the game starts. Pay attention to that before clicking the ready button the game hasn't started even if the spring engine has loaded and you're in game.

### Return values

none.
# Lua in SpringRTS/Callins/GamePreload
## GamePreload
### Return values

none.
# Lua in SpringRTS/Callins/GetTooltip
## GetTooltip
### Return values

vsx, vsy
# Lua in SpringRTS/Callins/Initialize
## Initialize
### Description

Runs once the script is loaded
# Lua in SpringRTS/Callins/Explosion
## Explosion
### Return values

weaponID, px, py, pz, ownerID"
# Lua in SpringRTS/Callins/FeatureCreated
## FeatureCreated
### Return values

featureID, allyTeam
# Lua in SpringRTS/Callins/GameFrame
## GameFrame
### Return values

frameNum
# Lua in SpringRTS/Callins/FeatureDestroyed
## FeatureDestroyed
### Return values

featureID, allyTeam
# Lua in SpringRTS/Callins/GameOver
## GameOver
### Description

Runs when the game ending condition is met

### Return values

[ [1] = allyTeamID1, [2] = allyTeamID2, ... ]
# Lua in SpringRTS/Callins/GroupChanged
## GroupChanged
### Description

Runs when the values in a group table change

### Return values

groupID
# LMIs in Control/Click here to continue/Controller synthesis/Hinf Optimal Output Controllability for Systems With Transients

$H_{\infty }$ Optimal Output Controllability for Systems With Transients
This LMI provides an $H_{\infty }$ optimal output controllability problem to check if such controllers for systems with unknown exogenous disturbances and initial conditions can exist or not.

## The System

    ${\begin{aligned}{\dot {x}}&=Ax+B_{1}v+B_{2}u,x(0)=x_{0},\\z&=C_{1}x+D_{11}v+D_{12}u,\\y&=C_{2}x+D_{21}v,\end{aligned}}$
where $x\in \mathbb {R} ^{n}$ is the state, $v\in \mathbb {R} ^{r}$ is the exogenous input, $u\in \mathbb {R} ^{m}$ is the control input, $y\in \mathbb {R} ^{p}$ is the measured output and $z\in \mathbb {R} ^{s}$ is the regulated output.

## The Data

System matrices $(A,B_{1},B_{2},C_{1},C_{2},D_{11},D_{12},D_{21},D_{22})$ need to be known. It is assumed that $v\in L_{2}[0,\infty )$. $N_{1},N_{2}$ are matrices with their columns forming the bais of kernels of $C_{2}D_{21}$ and $C_{2}D_{12}$ respectively.

## The Optimization Problem

For a given $\gamma$, the following $H_{\infty }$ condition needs to be fulfilled:
$\gamma _{w}=sup_{\|v\|_{\infty }^{2}+x_{0}^{\top }Rx_{0}\neq 0}{\frac {\|z\|_{\infty }}{(\|v\|_{\infty }^{2}+x_{0}^{\top }Rx_{0})^{1/2}}}<\gamma _{w},$

## The LMI: $H_{\infty }$ Output Feedback Controller for Systems With Transients

       ${\begin{aligned}&{\text{min}}_{\gamma ,X_{11},Y_{11}}:\gamma \\&{\text{subj. to: }}X_{11}>0,Y_{11}>0,\\&\quad {\begin{bmatrix}N_{1}&0\\0&I\end{bmatrix}}^{\top }{\begin{bmatrix}A^{\top }X_{11}+X_{11}A&X_{11}B_{1}&C_{1}^{\top }\\*&-\gamma ^{2}I&D_{11}^{\top }\\*&*&-I\end{bmatrix}}{\begin{bmatrix}N_{1}&0\\0&I\end{bmatrix}}<0,\\&\quad {\begin{bmatrix}N_{2}&0\\0&I\end{bmatrix}}^{\top }{\begin{bmatrix}AY_{11}+Y_{11}A^{\top }&Y_{11}C_{1}^{\top }&B_{1}\\*&-I&D_{11}\\*&*&-\gamma ^{2}I\end{bmatrix}}{\begin{bmatrix}N_{2}&0\\0&I\end{bmatrix}}<0,\\&\quad {\begin{bmatrix}X_{11}&I\\I&Y_{11}\end{bmatrix}}\geq 0,X_{11}<\gamma ^{2}R,\end{aligned}}$

## Conclusion:

Solution of the above LMI gives a check to see if an $H_{\infty }$ optimal output controller for systems with transients can exist or not.

## Implementation

A link to CodeOcean or other online implementation of the LMI

## Related LMIs

Links to other closely-related LMIs

## External Links

* LMI-based $H_{\infty }$-optimal control with transients Link to the original article.
# LMIs in Control/Click here to continue/Controller synthesis/Inverse Problem of Optimal Control

LMIs in Control/Click here to continue/Controller synthesis/Inverse Problem of Optimal Control
In some cases, it is needed to solve the inverse problem of optimal control within an LQR framework. In this inverse problem, a given controller matrix needs to be verified for the system by assuring that it is the optimal solution to some LQR optimization problem that is controllable and detectable. In other words: in this inverse problem, the controller is known and the LQR gain matrices are to be calculated such that the controller is the optimal solution.

## The System

The system is a linear time-invariant system, that can be represented in state space as shown below:
    ${\begin{aligned}{\dot {x}}&=Ax+Bu,\\z&={\begin{bmatrix}Q^{1/2}&0\\0&R^{1/2}\end{bmatrix}}{\begin{bmatrix}x\\u\end{bmatrix}}\end{aligned}}$
where $x\in R^{n},y\in R^{l},z\in R^{m}$ represent the state vector, the measured output vector, and the output vector of interest, respectively, $w\in R^{p}$ is the disturbance vector, and $A,B,C,Q,R$ are the system matrices of appropriate dimension. To further define: $x$ is $\in R^{n}$ and is the state vector, $A$ is $\in R^{n*n}$ and is the state matrix, $B$ is $\in R^{n*r}$ and is the input matrix, $w$ is $\in R^{r}$ and is the exogenous input, $C,Q,R$ is $\in R^{m*n}$ and are the output matrices, and $y$ and $z$ are $\in R^{m}$ and are the output and the output of interest, respectively.

## The Data

The matrices $A,B,C$ that define the system, and a given controller $K$ for which the inverse problem is to be solved.

## The Optimization Problem

In this LMI, the following cost function is to be minimized for a given controller K by finding an optimal input:
    ${\begin{aligned}\int _{0}^{\infty }z^{T}zdt\end{aligned}}$
the solution of the problem can be formulated as a state feedback controller given as:
    ${\begin{aligned}K&=-R^{-1}B^{T}P,\\A^{T}P+PA-PBR^{-1}B^{T}P+Q&=0\end{aligned}}$

## The LMI: Inverse Problem of Optimal Control

the inverse problem of optimal control is the following: Given a matrix $K$, determine if there exist $Q\geq 0$ and $R>0$, such that $(Q,A)$ is detectable and $u=Kx$ is the optimal control for the corresponding LQR problem. Equivalently, we seek $R>0$ and $Q\geq 0$ such that there exist $P$ nonnegative and $P_{1}$ positive-definite satisfying
    ${\begin{aligned}(A+BK)^{T}P+P(A+BK)+K^{T}RK+Q&=0\\B^{T}P+RK&=0\\A^{T}P_{1}+P_{1}A&<Q\end{aligned}}$

## Conclusion:

If the solution exists, then $K$ is the optimal controller for the LQR optimization on the matrices $Q$ and $R$

## Implementation

This implementation requires Yalmip and Sedumi.
https://github.com/rezajamesahmed/LMImatlabcode/blob/master/inverseprob.m

## Related LMIs

      * Multi-Criterion LQG]

## 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/Click here to continue/Controller synthesis/LMI for Decentralized Feedback Control

LMI for Decentralized Feedback Control
In large-scale systems like a multi-agent robotic system, national economies, or chemical refineries, an actuator should act based on local information, which necessitates a decentralized or distributed control strategy. In a decentralized control framework, the controllers are distributed and each controller has only access to a subset of local measurements. We describe LMI formulations for a general decentralized control framework and then provide an illustrative example of a decentralized control design.

## The System

In a decentralized controller design, the state feedback controller $u=Kx$ can be divided into $n$ sub-controllers $u_{i}=K_{i}x_{i},\quad i=1,2,...,n$.

## The Data

A general state space representation of a linear time-invariant system is as follows:
${\begin{aligned}&{\dot {x}}=Ax+Bu\\&y=Cx+Du\end{aligned}}$
where $x$ is a $n\times n$ vector of state variables, $B$ is the input matrix, $C$ is the output matrix, and $D$ is called the feedforward matrix. We assume that all the four matrices, $A$, $B$, $C$, and $D$ are given.

## The Optimization Problem

We aim to solve the $H_{\infty }$-optimal full-state feedback control problem using a controller $u=Kx$.
In a decentralized fashion, the control input $u$ can be divided into sub-controllers $u_{1},u_{2},...,u_{j}$ and can be written as $u=[u_{1}\quad u_{2}\quad ...\quad u_{j}]_{1\times n}^{\text{T}}$.
For instance, let $j=3$ and $n=6$. Thus, there are three control inputs $u_{1}$, $u_{2}$, and $u_{3}$. We also assume that u_{1} only depends on the first and the second states, while $u_{2}$ and $u_{3}$ only depend on thrid to sixth states. For this example, the controller gain matrix can be described by:
$K={\begin{bmatrix}k_{1}&k_{2}&0&0&0&0\\0&0&k_{3}&k_{4}&k_{5}&k_{6}\\0&0&k_{7}&k_{8}&k_{9}&k_{10}\\\end{bmatrix}}$
Thus, the decentralized controller gain consists of sub-matrices of gains.

## The LMI: LMI for decentralized feedback controller

The mathematical description of the LMI formulation for a decentralised optimal full-state feedback controller can be described by:
${\begin{aligned}&{\text{min}}\quad \gamma \\&{\begin{bmatrix}YA^{\text{T}}+AY+Z^{\text{T}}B_{2}^{\text{T}}+B_{2}Z&*^{T}&*^{T}\\B_{1}^{T}&-\gamma I&*^{T}\\YC_{1}^{T}+Z^{T}D_{12}&D_{11}&-\gamma I\end{bmatrix}}\end{aligned}}$
where $Y>0$ is a positive definite matrix and $Z$ such that the aforemtntioned constraints in LMIs are satisfied.

## Conclusion:

The controller gain matrix is defined as:
$K={\begin{bmatrix}0&0\\0&F\end{bmatrix}}$
where $F$ can be found after solving the LMIs and obtaining the variables matrices $Y$ and $Z$. Thus,
$F=ZY^{-1}$.

## Implementation

A link to Matlab codes for this problem in the Github repository:
https://github.com/asalimil/LMI_for_decentralized_feedback_controller/tree/master

## External Links

A list of references documenting and validating the LMI.
* - LMI in Control Systems Analysis, Design and Applications

## Return to Main Page

LMIs in Control/Tools
# LMIs in Control/Click here to continue/Controller synthesis/H-inf Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

LMIs in Control/Click here to continue/Controller synthesis/H-inf Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty
If there exists some $\mu \geq 0,P>0$, and $Z$ such that the LMI holds, then the system satisfies $\|y\|_{L_{2}}\leq \gamma \|u\|_{L_{2}}.$ There also exists a controller with $u(t)=Kx(t).$

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t)+Mp(t)+B_{2}w(t),&&p(t)=\Delta (t)q(t),\\q(t)&=Nx(t)+D_{12}u(t),&&\Delta \in \mathbf {\Delta } \;:=\{\Delta \in \mathbb {R} ^{n\times n}:\|\Delta \|\leq 1\}\\y(t)&=Cx(t)+D_{22}u(t)\\\end{aligned}}$

## The Data

The matrices $A,B,M,B_{2},N,D_{12},C,D_{22}$.

## The Optimization Problem

Minimize $\gamma$ subject to the LMI constraints below.

## The LMI:

       ${\begin{aligned}{\text{Find}}\;&P>0,\mu \geq 0,{\text{ and }}Z:\\{\begin{bmatrix}AP+BZ+PA^{T}+Z^{T}B^{T}+B_{2}B_{2}^{T}+\mu MM^{T}&(CP+D_{22}Z)^{T}&PN^{T}+Z^{T}D_{12}^{T}\\CP+D_{22}Z&-\gamma ^{2}I&0\\NP+D_{12}Z&0&-\mu I\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

The controller gains, K, are calculated by $K=ZP^{-1}$.

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

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.