OpenLLM-France/wikimedia huggingface dataset:
# KS3 Computing/Logic/What is logic
#### What is Logic?

When we talk about logic in computing we normally mean a variety of logic called Boolean Logic, named for George Boole,
an English mathematician. It is only concerned with whether things are True or False. This matches well onto digital computers which have circuits that are either on or off. Logic is used in the design of computer chips as well in programs written to run on computers. Other areas where logic might be used are in the operation of traffic lights (you don't want traffic flowing both ways across a junction at the same time) and in many safety systems (e.g. operation of a spaceship's airlock) where the logic may be implemented mechanically rather than electronically.
# 103.6 Modify Process Execution Priorities

Candidates should be able to manage process execution priorities.
Key Knowledge Areas
* Know the default priority of a job that is created.
* Run a program with higher or lower priority than the default..
* Change the priority of a running process.
Process Priority
When a process is started by a user it has a default priority, or nice number of 0. Nice numbers (NI) alter the CPU priority and are used to balance the CPU load in a multiuser environment. Nice numbers range from 19 [lowest] to -20 [highest].
Only root can decrease the nice number of a process. Since all processes start with a default nice number of zero as a consequence negative nice numbers can only be set by root!
To modify a process' priority that is already running use renice. To set a process' priority use nice.
Syntax
Notice that renice works with PIDs and handles lists of processes at a time. A useful option to renice is the -u option which affects all processes run by a user.
Set nice number 1 for processes 234 and 765:
# renice +1 -p 234 765
Set nice number -5 for xclock:
# nice --5 xclock
Continuously updating process information
The top utility will update information on processes at an adjustable rate. While top is running you can type h for a list of commands. The space bar will update information instantly. You can also use top to change a process' priority as we shall see in the next section. Top provides a convenient summary of number of processes, users, length of time the machine has been up and the load average for the past 5, 10 and 15 minutes. You can also obtain this information once off with the uptime command. Below is an example of the output you can expect from running this command.
13:21:48 up 5:54, 1 user, load average: 0.92, 0.70, 0.66
Here 13:21 is the current time, 5:54 is the length of time the machine has been up, 1 user is logged in and the load average for the past 5,10 and 15 minutes is 0.82, 0.70 and 0.66.
Used files, terms and utilities:
* nice
* ps
* renice
* top
Previous Chapter | Next Chapter
# Introduction

This module sets the scene for “The African FOSS Business Models for ICT-based SMEs” by providing a basic introduction to the phenomenon that has come to be known as Free and Open Source Software or FOSS. The concept of FOSS is becoming more mainstream to the public and we are seeing increased business adoption which is generating higher levels of revenue. FOSS is no longer a marginal concept but rather it has become good business. This module sets the scene for exploring various FOSS concepts ranging from terms and definitions, the organizational structures of projects and communities, to the global business impact of FOSS which could form the basis for understanding and constructing business models within the African context.

# Learning Objectives

* Gain a basic understanding of FOSS.
* Understand and appreciate how FOSS projects and communities work
* Develop confidence in their ability to run FOSS business.
* Understand the changing nature of FOSS business.
* Understand the types of existing and emerging FOSS business models.
* Be able to identify the potential local markets for FOSS business.
* Gain knowledge of the leading online resources to keep current in the FOSS eco-space.
* Identify the FOSS licensing models

# Pool of African ict@innovation expert trainers

| | Name Module | Name |
| Module 1 | Introduction to Emerging: FLOSS Business Models | James Njenga, Fred Jeboah, Shirley Akasreku More Trainers per country in full Pool of Trainers http://www.ict-innovation.fossfa.net/wiki/public-wiki/course-advanced-african-foss-business-models/FBMTrainers |
Main contributors
| Module 1 | Sulayman K. Sowe,Nhlanhla Mabaso,Frank Tilugulilwa,Irene Fernández Monsalve,Samer Azmy,Kim Tucker,Glenn McKnight |
Additional material for Module 1: Introduction to Emerging FLOSS Business Models (presentations, tests, evaluation forms, pool of trainers, derived material) is available online at:
http://www.ict-innovation.fossfa.net/node/4252

# Sessions and Timetable

The entire content in this Module is estimated to be delivered in 1 day, with some variations within the modules. For instructional purpose, the content of this Module can be delivered as proposed in the summarized table below.
| Time | Session |
| 9:00 – 10:30 | * Introduction to Module 1 General FOSS Concepts |
| 10:30 - 10:45 | Coffee Break |
| 10:45 - 12:15 | * FOSS Business Globally Evolution of FOSS Communities and Software Markets |
| 12:15- 13:30 | Lunch |
| 13:30 - 15:00 | * Evolution of FOSS Communities and Software Markets-Contd Multimedia listening comprehension Leading FOSS resources for keeping current on the FLOSS eco-space |
| 15:00 – 15:15 | Coffee Break |
| 15:15 - 17:00 | * FOSS License End of Module Evaluation |
Previous Chapter | Next Chapter
# Ict@innovation: Free your IT Business in Africa

If you prefer the ODT version or you would like to print the contents you see below please click here.

## Table of Contents
### Module 1: Introduction to emerging FOSS Business Models

* 1.1 General FOSS Concepts
* 1.1 General FOSS Concepts
* 1.2 FOSS Business Globally
* 1.3 Evolution of FOSS Communities and Software Markets
* 1.4 FOSS Licensing Models
* 1.5 FOSS resources for keeping current on the FOSS eco-Space
* 1.6 Multimedia
* 1.7 References
* 1.8 Assignments and Answers
* 1.9 Test Module 1

### Module 2: African FOSS Business Models: Case Studies

* 2.1 The OpenWorld Ltd Experience
* 2.2 The case of GIS Global Image Ltd.
* 2.3 Revitalizing software resources through FOSS
* 2.4 Training Linux Users in South Africa
* 2.5 The Linux Solutions Experience
* 2.6 The Amest Santim Systems PLC Experience
* 2.7 CENFOSS - Using FOSS for Business
* 2.8 FOSS Business Potentials: From Academic to Business
* 2.9 Taxonomy of FOSS Business Models
* 2.10 2.1-2.8 Assessment
* 2.11 Assignments and Answers
* 2.12 Test Module 2

### Module 3: Communicating FOSS

* 3.1 Public Relation and Advocacy Strategies
* 3.2 Advocating FOSS
* 3.3 Online Advocacy tools
* 3.4 Creating a FOSS market and brand in Africa
* 3.5 Assignments and Answers
* 3.6 Test Module 3

### Module 4: Introduction to General Business Skills

* 4.1 Starting a Business
* 4.2 Defining Target Market
* 4.3 Leadership
* 4.4 Organizational Structuring
* 4.5 FOSS Proposals and Contracts
* 4.6 References
* 4.7 Assignments

### Module 5: FOSS Business Knowledge and Skills

* 5.1 How FOSS business is different from other types of business
* 5.2 FOSS Communities
* 5.3 Competition, cooperation – coopetition
* 5.4 Marketing FOSS
* 5.5 FOSS Strategies
* 5.6 Innovation in FOSS Business
* 5.7 References
* 5.8 Assignments
* 5.9 Test Module 5

### Module 6: FOSS Training

* 6.1 How to be a FOSS Trainer
* 6.2 FOSS Training as a Business
* 6.3 Organising Trainings
* 6.4 Open Educational Resources and Open Content
* 6.5 Communication Skills
* 6.6 Assignments and Answers
* 6.7 Test Module 6
# LMIs in Control/pages/H stabilization

$\mathbb {H} _{(\alpha ,\beta )}$-Stabilization
There are a wide variety of control design problems that are addressed in a wide variety of different ways. One of the most important control design problem is that of state feedback stabilization. One such state feedback problem, which will be the main focus of this article, is that of $\mathbb {H} _{(\alpha ,\beta )}$-Stabilization, a form of $\mathbb {D}$-Stabilization where the real components are located on the left-half of the complex plane.

## The System

For this particular problem, suppose that we were given a linear system in the form of:
    ${\begin{aligned}{\dot {x}}&=Ax+Bu,\\\end{aligned}}$
where $x\in \mathbb {R} ^{n}$ and $u\in \mathbb {R} ^{r}$. Then the LMI for determining the $\mathbb {H} _{(\alpha ,\beta )}$-stabilization case would be obtained as described below.

## The Data

In order to obtain the LMI, we need the following 2 matrices: $A{\text{ and }}B$.

## The Optimization Problem

Suppose - for the linear system given above - we were asked to design a state-feedback control law where $u=Kx$ such that the closed-loop system:
    ${\begin{aligned}{\dot {x}}&=(A+BK)x\\\end{aligned}}$
is $\mathbb {H} _{(\alpha ,\beta )}$ stable, then the system would be stabilized as follows.

## The LMI: $\mathbb {H} _{(\alpha ,\beta )}$-Stabilization

From the given pieces of information, it is clear that the optimization problem only has a solution if there exists a matrix $W$ and a symmetric matrix $P>0$ that satisfy the following:
       ${\begin{aligned}{\begin{cases}AP+P{A^{T}}+BW+{W^{T}}{B^{T}}+2{\alpha }P&<0\\-AP-P{A^{T}}-BW-{W^{T}}{B^{T}}-2{\beta }P&<0\end{cases}}\end{aligned}}$

## Conclusion:

Given the resulting controller matrix $K=WX^{-1}$, it can be observed that the matrix is $\mathbb {H} _{(\alpha ,\beta )}$-stable.

## Implementation

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

## Related LMIs

      * D stabilization - Equivalent LMI for $\mathbb {D} _{(q,r)}$-stabilization.

## 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 - A book co-authored by Guang-Ren Duan and Hai-Hua Yu.
# LMIs in Control/pages/Hankel Norm for Affine Parametric Varying Systems
## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+B_{w}w(t),\\z(t)&=C_{z}(\theta )x(t)+D_{zw}(\theta )w(t),\end{aligned}}$
where $C_{z}$ and $D_{zw}$ depend affinely on parameter $\theta \in \mathbb {R} ^{p}$.

## The Data

The matrices $A,B_{w},C_{z}(.),D_{zw}(.)$.

## The Optimization Problem:

Solve the following semi-definite program
       ${\begin{aligned}&\min _{\{Q\succeq 0,\gamma ^{2},\theta \}}\gamma ^{2}\\&\quad s.t.\quad D_{zw}(\theta )=0,\quad A^{\top }Q+QA+C_{z}(\theta )C_{z}(\theta )\preceq 0,\quad \gamma ^{2}I-W_{c}^{1/2}QW_{c}^{1/2}\succeq 0,\end{aligned}}$
where $W_{c}$ is the controllability Gramian, i.e., $W_{c}\triangleq \int _{0}^{\infty }e^{At}B_{w}B_{w}^{\top }e^{A^{\top }t}dt$.

## Implementation

https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/0faedcdd9fba92bc27a318d80159c04a0b342f35

## Conclusion

The Hanakel norm (i.e., the square root of the maximum eigenvalue) of $H_{\theta }$ is less than ${\gamma }$ if and only if the above LMI holds and the value function returns the maximum provable Hankel norm.

## Remark

$D_{zw}$ is assumed to be zero.

## 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/pages/Hurwitz detectability

LMIs in Control/pages/Hurwitz detectability

## Hurwitz Detectability

Hurwitz detectability is a dual concept of Hurwitz stabilizability and is defined as the matrix pair $(A,C)$, is said to be Hurwitz detectable if there exists a real matrix $L$ such that $A+LC$ is Hurwitz stable.

## The System

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

## The Data

* The matrices $A,B,C,D$ are system matrices of appropriate dimensions and are known.

## The Optimization Problem

There exist a symmetric positive definite matrix $P$ and a matrix $W$ satisfying $A^{T}P+PA+W^{T}C+C^{T}W<0$
There exists a symmetric positive definite matrix $P$ satisfying
$N_{c}^{T}(A^{T}P+PA)N_{c}<0$
with $N_{c}$ being the right orthogonal complement of $C$.
There exists a symmetric positive definite matrix $P$ such that
$A^{T}P+PA<\gamma C^{T}C$
for some scalar $\gamma >0$

## The LMI:

Matrix pair $(A,C)$, is Hurwitz detectable if and only if following LMI holds
* $A^{T}P+PA+W^{T}C+C^{T}W<0.$
* $N_{c}^{T}(A^{T}P+PA)N_{c}<0$
* $A^{T}P+PA-\gamma C^{T}C<0$

## Conclusion:

Thus by proving the above conditions we prove that the matrix pair $(A,C)$ is Hurwitz Detectable.

## Implementation

Find the MATLAB implementation at this link below Hurwitz detectability

## Related LMIs

Links to other closely-related LMIs LMI for Hurwitz stability LMI for Schur stability Schur Detectability

## 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.

## Return to Main Page:

* https://en.wikibooks.org/wiki/LMIs_in_Control
# LMIs in Control/pages/Hinfinityoptimalfilter

Optimal filtering is a means of adaptive extraction of a weak desired signal in the presence of noise and interfering signals. The goal of optimal filtering is to design a filter that acts on the output $z$ of the generalized plant and optimizes the transfer matrix from w to the filtered output.

## The System:

Consider the continuous-time generalized LTI plant with minimal states-space realization
    ${\begin{aligned}{\dot {x}}&=Ax+B_{1}w\\z&=C_{1}x+D_{11}w,\\y&=C_{2}x+D_{21}w,\end{aligned}}$
where it is assumed that $A$ is Hurwitz.

## The Data

The matrices needed as inputs are $A,B_{1},C_{2},C_{1},,D_{11},D_{21}$.

## The Optimization Problem:

An $H\infty$-optimal filter is designed to minimize the $H_{\infty }$ norm of ${\tilde {P}}(s)$ in following equation.
    ${\begin{aligned}{\tilde {P}}(s)={\tilde {C}}_{1}(sI-{\tilde {A}})^{-}1{\tilde {B}}_{1}+{\tilde {D}}_{11},\\{\text{where}}\\{\tilde {A}}={\begin{bmatrix}A&&0\\B_{f}C_{2}&&A_{f}\end{bmatrix}}&<0\\{\tilde {B}}_{1}={\begin{bmatrix}B_{1}\\B_{f}D_{21}\end{bmatrix}}&<0\\{\tilde {C}}_{1}={\begin{bmatrix}C_{1}-D_{f}C_{2}-C_{f}\end{bmatrix}}&<0\\{\tilde {D}}_{11}=D_{11}-D_{f}D_{21}\\\end{aligned}}$

## The LMI: $H_{\infty }$- Optimal filter

Solve for $A_{n}\in \mathbb {R} ^{n_{x}\times n_{x}},B_{n}\in \mathbb {R} ^{n_{x}\times n_{y}},C_{f}\in \mathbb {R} ^{n_{x}\times n_{x}}$, $X,Y\in \mathbb {S} ^{n_{x}}$ and $\nu \in \mathbb {R} _{>0}$ that minimize $\zeta (\nu )=\nu$ subject to $X>0,Y>0$.
       ${\begin{aligned}{\begin{bmatrix}YA+A^{T}Y+B_{n}C_{2}&&A_{n}+C_{2}^{T}B_{n}^{T}+A^{T}X&&YB_{1}+B_{n}D_{21}&&{C_{1}}^{T}-{C_{2}}^{T}{D_{f}}^{T}\\\star &&A_{n}+A_{n}^{T}&&XB_{1}+B_{n}D_{21}&&-{C_{f}}^{T}\\\star &&\star &&-\gamma I&&{D_{1}1}^{T}-{D_{2}1}^{T}{D_{f}}^{T}\\\star &&\star &&\star &&-\gamma I\end{bmatrix}}&<0\\\\Y-X>0\\\end{aligned}}$

## Conclusion:

The filter is recovered by $A_{f}=X^{-1}A_{n}$ and $B_{f}=X^{-1}B_{n}$.

## Implementation

* https://github.com/Ricky-10/coding107/blob/master/Hinfinity%20Optimal%20filter- $H\infty$- Optimal Filter

## External links

* - Optimal Filtering
* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
# LMIs in Control/pages/Hinf Output Optimal Control

$H_{\infty }$ 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/pages/HInf Optimal Observer

$H\infty$-Optimal observers yield robust estimates of some or all internal plant states by processing measurement data. Robust observers are increasingly demanded in industry as they may provide state and parameter estimates for monitoring and diagnosis purposes even in the presence of large disturbances such as noise etc. It is there where Kalman filters may tend to fail. State observer is a system that provides estimates of internal states of a given real system, from measurements of the inputs and outputs of the real system. The goal of $H_{\infty }$ -optimal state estimation is to design an observer that minimizes the $H_{\infty }$ norm of the closed-loop transfer matrix from w to z.

## The System

Consider the continuous-time generalized plant $P$ with state-space realization
    ${\begin{aligned}{\dot {x}}&=Ax+B_{1}w,\\y&=C_{2}x+D_{21}w\\\end{aligned}}$

## The Data

The matrices needed as input are $A,B_{1},B_{2},C_{2},D_{21},D_{11}$.

## The Optimization Problem

The observer gain $L$ is to be designed such that the $H\infty$ of the transfer matrix from w to z, given by
    ${\begin{aligned}T(s)=C_{1}(s1-(A-LC_{2}))^{-1}(B_{1}-LD_{21})+D_{11}\\\end{aligned}}$
is minimized. The form of the observer would be:
    ${\begin{aligned}{\dot {\hat {x}}}=A{\hat {x}}+L(y-{\hat {y}}),\\{\hat {y}}=C_{2}{\hat {x}}\\\end{aligned}}$

## The LMI: $H_{\infty }$ Optimal Observer

The $H\infty$-optimal observer gain is synthesized by solving for $P\in \mathbb {S} ^{n_{x}},G\in \mathbb {R} ^{n_{x}\times n_{y}}$, and $\gamma \in \mathbb {R} _{>0}$ that minimize $\zeta (\gamma )=\gamma$ subject to $P>0$ and
       ${\begin{aligned}{\begin{bmatrix}PA+A^{T}P-GC_{2}-{C_{2}}^{T}G^{T}&&PB_{1}-GD_{21}&&C_{1}^{T}\\\star &&-\gamma 1&&{D_{11}}^{T}\\\star &&\star &&-\gamma 1\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

The $H_{\infty }$ -optimal observer gain is recovered by $L=P^{-1}G$ and the $H_{\infty }$ norm of T(s) is $\gamma$.

## Implementation

Link to the MATLAB code designing $H\infty$- Optimal Observer
https://github.com/Ricky-10/coding107/blob/master/HinfinityOptimalobserver

# 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/pages/H infinity Norm for Affine Parametric Varying Systems
## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+B_{w}w(t),\\z(t)&=C_{z}(\theta )x(t)+D_{zw}(\theta )w(t),\end{aligned}}$
where $C_{z}$ and $D_{zw}$ depend affinity on parameter $\theta \in \mathbb {R} ^{p}$.

## The Data

The matrices $A,B_{w},C_{z}(.),D_{zw}(.)$.

## The Optimization Problem:

Solve the following semi-definite program
       ${\begin{aligned}&\min _{\{P\succ 0,\gamma \geq 0\}}\gamma \\&\quad s.t.{\begin{bmatrix}A^{\top }P+PA&PB_{w}\\B_{w}^{\top }P&-\gamma ^{2}I\end{bmatrix}}+{\begin{bmatrix}C_{z}^{\top }(\theta )\\D_{zw}^{\top }(\theta )\end{bmatrix}}{\begin{bmatrix}C_{z}(\theta )&D_{zw}(\theta )\end{bmatrix}}\preceq 0.\end{aligned}}$

## Implementation

https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/5462bc1dc441bc298d50a2c35075e9466eba8355

## Conclusion

The value function of the above semi-definite program returns the ${\mathcal {H}}_{\infty }$ norm of the system.

## Remark

It is assumed that $A$ is stable and $(A,B_{w})$ is controllable and the semi-infinite convex constraint $\|H_{\theta }(j\omega )\|<\gamma$ for all $\omega \in \mathbb {R}$, is converted into a finite-dimensional convex LMI.

## 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.
# Introduction to Information Literacy in the K12 Classroom/Forward

Introduction to Information Literacy in the K12 Classroom/Table of Contents

## Forward

The development of this book is part of an education course, ITEC521 Information Literacy in the Digital Age, at the University of Mary Washington College of Graduate and Professional Studies in Fredericksburg, VA. The book's primary Contributors are graduate students and preservice teachers.
The goal of this project is two fold;
* to create a student-authored textbook that highlights important concepts as they relate to information literacy in the digital age that can be utilized by K12 teachers around the world, and
* to empower each teacher author with knowledge of digital literacy, effective communication, collaborative participation, and the idea that technology is an effective tool as it relates to each of these skills that can be transfered into their classroom.
Please take time to explore this book and let us know what you think. The Discussion tab on each page or the Talk tab are two locations within our book that you can leave comments, suggestions, or information pertaining to particular authors, content, or pages themselves. We look forward to your participation and feedback.
Each chapter of this book was researched and written by one to two students and edited by the entire class. Each section has media added to enhance the content and meaning on each page. The supplemental section for each chapter will provide any worksheets or additional information that was deemed important for that particular chapter.
Thank you for taking a look at our book we hope you find it useful and meaningful.