OpenLLM-France/wikimedia huggingface dataset:
# LMIs in Control/LMIs for Hurwitz Stability

LMIs in Control/LMIs for Hurwitz Stability
This is a set of LMI conditions for determining Hurwitz Stability of continuous time systems.

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t),\\y(t)&=Cx(t)+Du(t)\\\end{aligned}}$

## The Data

* The matrices $A,B,C,D$ are system matrices of appropriate dimensions.
* $x\in \mathbb {R} ^{n}$, $y\in \mathbb {R} ^{m}$ and $u\in \mathbb {R} ^{r}$ are state vector, output vector and input vector respectively.

## The Optimization Problem

Find a symmetric postive definite matrix $X$, where $X\in \mathbb {R} ^{n}$. Thus $X>0$ and $K=ZX^{-1}$ where $Z\in \mathbb {R} ^{r}$.

## The LMI: The Lyapunov Inequality

Matrix pair $(A,B)$, is Hurwitz stabilizable if and only if there exist a symmetric positive definite matrix $X$ and a matrix $Z$ satisfying $AX+XA^{T}+BZ+Z^{T}B^{T}<0$
Proof : Matrix pair $(A,B)$, is Hurwitz stabilizable if and only if
$rank[sI-AB]=n$, $\forall s\in \lambda (A)$ and $Re(s)\geq 0$
This is the definition of Hurwitz Stability. Now, using this definition we can prove the above LMI if we find matrix $X>0$ and matrix $Z$ and thus by substituting $Z=KX$ in the above LMI we get,
$(A+BK)X+X(A+BK)^{T}<0$, which brings us to the Lyapunov Stability Theory.

## Conclusion:

Thus by proving the above conditions we prove that the matrix pair $(A,B)$ is Hurwitz Stabilizable. At the same time, we also prove that the $rank[sI-AB]=n$ i.e. it is full rank and the real part of $s$ is $>0$.

## Implementation

Please find the MATLAB implementation at this link below https://github.com/omiksave/LMI

## Related LMIs

Links to other closely-related LMIs
* Schur Stability
* Quadratic Hurwitz Stability
* Quadratic Schur Stability
* Quadratic D-Stability

## 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/Linear matrix inequalities and control theory/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(Variable)
* 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
** Nonstrict Projection Lemma
** Reciprocal Projection Lemma
** Projection Lemma-Based Properties
* Ellipsoidal Inequality
* Continuous Time Properties
** Schur Complement
*** Strict and Nonstrict Schur Complement
*** Schur Complement Lemma-Based Properties
** Eigenvalue related Problems
*** LMI for Eigenvalue Minimization
*** Eigenvalue Problem
*** LMI for Generalized Eigenvalue Problem
** LMI for Matrix Norm Minimization
** LMI for Generalized Eigenvalue Problem
** LMI for Linear Programming
** LMI for Feasibility Problem
** Structured Singular Value
** LMI for Minimizing Condition Number of Positive Definite Matrix
** Continuous Quadratic Stability
* 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
# LMIs in Control/Linear matrix inequalities and control theory/pages/Basic Matrix Theory
## Basic Matrix Notation

Consider the complex matrix $A\in \mathbb {C} ^{n\times m}$.
       $A={\begin{bmatrix}a_{11}&\dots &a_{1m}\\\vdots &\ddots &\vdots \\a_{n1}&\dots &a_{nm}\end{bmatrix}}\in \mathbb {C} ^{n\times m}$
Transpose of a Matrix
The transpose of $A$, denoted as $A^{T}$ or $A'$ is:
       $A^{T}={\begin{bmatrix}a_{11}&\dots &a_{n1}\\\vdots &\ddots &\vdots \\a_{1m}&\dots &a_{nm}\end{bmatrix}}\in \mathbb {C} ^{m\times n}.$
Adjoint of a Matrix
The adjoint or hermitian conjugate of $A$, denoted as $A^{*}$ is:
       $A^{*}={\begin{bmatrix}a_{11}^{*}&\dots &a_{n1}^{*}\\\vdots &\ddots &\vdots \\a_{1m}^{*}&\dots &a_{nm}^{*}\end{bmatrix}}\in \mathbb {C} ^{m\times n}.$
Where $a_{nm}^{*}$ is the complex conjugate of matrix element $a_{nm}$.
Notice that for a real matrix $A\in \mathbb {R} ^{n\times m}$, $A^{*}=A^{T}$.

## Important Properties of Matricies

Hermitian, Self-Adjoint, and Symmetric Matricies
A square matrix $A\in \mathbb {C} ^{n\times n}$ is called Hermitian or self-adjoint if $A=A^{*}$.
If $A\in \mathbb {R} ^{n\times n}$ is Hermitian then it is called symmetric.
Unitary Matricies
A square matrix $A\in \mathbb {C} ^{n\times n}$ is called unitary if $A^{*}=A^{-1}$ or $A^{*}A=I$.

## 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/LMIs for Controller Synthesis/H-infinity Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

LMIs in Control/LMIs for Controller Synthesis/H-infinity Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

## 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

${\text{Minimize }}\gamma$

## The LMI: The Lyapunov Inequality

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

## Conclusion:

${\begin{aligned}{\text{If there exists some }}\mu \geq 0,P>0,{\text{ and }}Z{\text{ such that the above LMI holds, then the system satisfies }}||y||_{L_{2}}\leq \gamma ||u||_{L_{2}},\\{\text{ and there exists a controller with }}u(t)=Kx(t){\text{ where }}K=ZP^{-1}{\text{ is the corresponding controller.}}\end{aligned}}$

## 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.
# LMIs in Control/LMI for Polytopic Uncertainity/Polytopic Quadratic Stability

LMIs in Control/LMI for Polytopic Uncertainity/Polytopic Quadratic Stability
The System: Consider the system with Affine Time-Varying
uncertainty (No input)
    ${\begin{aligned}{\dot {x}}(t)&=(A_{0}+\Delta A(t))x(t)\\\end{aligned}}$
where
    ${\begin{aligned}\Delta A(t)=A_{1}\delta _{1}(t)+....+A_{k}\delta _{k}(t)\end{aligned}}$
where $\delta _{i}(t)$ lies in either the intervals
    ${\begin{aligned}\delta _{i}\in [\delta _{i}^{-},\delta _{i}^{+}]\end{aligned}}$
or the simplex
    ${\begin{aligned}\delta (t)\in {\delta :\Sigma \alpha _{i}=1,\alpha \geq 0}\end{aligned}}$
The LMI: Polytopic Quadratic Stability
The system is Quadratically Stable over $\Delta$ if there exists a P > 0
Interpretation of the results of the LMI
Implementation A link to CodeOcean or other online implementation of the LMI
Related LMIs
Links to other closely-related LMIs
External Links
A list of references documenting and validating the LMI.
* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* 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:
Related LMIs:
# LMIs in Control/LMI for Polytopic Uncertainity/Quadratic Polytopic Hinf- Optimal State Feedback Control

LMIs in Control/LMI for Polytopic Uncertainity/Quadratic Polytopic Hinf- Optimal State Feedback Control
The System:
Consider System with following state-space representation.
    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+B_{1}q(t)+B_{2}w(t)\\p(t)&=C_{1}x(t)+D_{11}q(t)+D_{12}w(t)\\z(t)&=C_{2}x(t)+D_{21}q(t)+D_{22}w(t)\\\end{aligned}}$
Add uncertainty to system matrices
    $A,B_{1},B_{2},C_{1},C_{2},D_{11},D_{12}$
New state-space representation
    ${\begin{aligned}{\dot {x}}(t)&=(A+A_{i})x(t)+(B_{1}+B_{i})q(t)+(B_{2}+B_{i})w(t)\\p(t)&=(C_{1}+C_{i})x(t)+(D_{11}+D_{i})q(t)+(D_{12}+D_{i})w(t)\\z(t)&=C_{2}x(t)+D_{21}q(t)+D_{22}w(t)\\\end{aligned}}$
The Optimization Problem:
Recall the closed-loop in state feedback is:
$S(P,K)=$
       ${\begin{aligned}{\begin{bmatrix}A+B_{2}2F&&B_{1}\\C_{1}+D_{12}F&&D_{11}\end{bmatrix}}\\\end{aligned}}$
This problem can be formulated as $H\infty$ optimal state-feedback, where K is a controller gain matrix.
The LMI: An LMI for Quadratic Polytopic $H\infty$ Optimal State-Feedback Control
$||S(P(\Delta ),K(0,0,0,F))||_{H\infty }\leq \gamma$
$Y>0$
       ${\begin{aligned}{\begin{bmatrix}Y(A+A_{i})^{T}+(A+A_{i})Y+Z^{T}(B_{2}+B_{1,i})^{T}+(B_{2}+B_{1,i})Z&&*^{T}&&*^{T}\\(B_{1}+B_{1,i})^{T}&&-\gamma I&&*^{T}\\(C_{1}+C_{1,i})Y+(D_{12}+D_{12,i})Z&&(D_{11}+D_{11,i})&&-\gamma I\end{bmatrix}}<0\end{aligned}}$
Conclusion:
The $H\infty$ Optimal State-Feedback Controller is recovered by $F=ZY^{-1}$
Implementation: https://github.com/JalpeshBhadra/LMI/tree/master
Related LMIs:
# LMIs in Control/LMIs for Controller Synthesis/Optimal State-Feedback Controllers with Structured Norm-Bounded Uncertainty

LMIs in Control/LMIs for Controller Synthesis/Optimal State-Feedback Controllers with Structured Norm-Bounded Uncertainty

## The System

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

## The Data

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

## The Optimization Problem

${\text{Minimize }}\gamma$

## The LMI: The Lyapunov Inequality

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

## Conclusion:

${\begin{aligned}{\text{If there exists some }}\Theta \in P\Theta ,P>0,{\text{ and }}Z{\text{ such that the above LMI is feasible, then the system satisfies }}||y||_{L_{2}}\leq \gamma ||u||_{L_{2}}.\\{\text{and there exists a controller with }}u(t)=Kx(t){\text{ where }}K=ZP^{-1}{\text{ is the corresponding controller.}}\end{aligned}}$

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty
H-infinity Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty
Stabilizing 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.
# LMIs in Control/LMIs for Controller Synthesis/Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

LMIs in Control/LMIs for Controller Synthesis/Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

## 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: The Lyapunov Inequality

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

## Conclusion:

${\begin{aligned}{\text{If the system is quadratically stable, then there exists some }}\mu \geq 0,P>0,{\text{ and }}Z{\text{ such that the above LMI is feasible.}}\\{\text{ Also there exists a controller for the system with }}u(t)=Kx(t){\text{ where }}K=ZP^{-1}{\text{ is the quadratically stabilizing controller.}}\end{aligned}}$

## 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.
# LMIs in Control/LMIs for Controller Synthesis/Stabilizing State-Feedback Controllers with Structured Norm-Bounded Uncertainty

LMIs in Control/LMIs for Controller Synthesis/Stabilizing State-Feedback Controllers with Structured Norm-Bounded Uncertainty

## The System

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

## The Data

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

## The LMI: The Lyapunov Inequality

       ${\begin{aligned}{\text{Find}}\;&P>0,Z:\\{\begin{bmatrix}AP+BZ+PA^{T}+Z^{T}B^{T}&PN^{T}+Z^{T}D_{12}^{T}\\NP+D_{12}Z&0\end{bmatrix}}+{\begin{bmatrix}M\Theta M^{T}&M\Theta Q^{T}\\Q\Theta M^{T}&Q\Theta Q^{T}-\Theta \end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

${\begin{aligned}{\text{The system is quadratically stable if and only if there exists some }}\Theta \in P\Theta ,P>0,{\text{ and }}Z{\text{ such that the above LMI is feasible.}}\\{\text{Furthermore, there exists a controller with }}u(t)=Kx(t){\text{ where }}K=ZP^{-1}{\text{ is the quadratically stabilizing controller.}}\end{aligned}}$

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty
H-infinity Optimal Quadratically Stabilizing Controllers with Parametric 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.
# Pokémon/Pokédex/Weavile
## Description

A bipedal Pokémon.

## Base Statistics

A Dark and Ice type Pokémon.

## Type Matching

Moves that deal 400% of their damage to Weavile: fighting Moves that deal 200% of their damage to Weavile: bug, fairy, fire, rock, steel Moves that deal 50% of their damage to Weavile: ghost, dark, ice Moves that deal 0% of their damage to Weavile: psychic
# Pokémon/Pokédex/Weedle
## Basic Statistics

* National Index: 13
* Johto Index: 27
* Hoenn Index: 215
* Stage: Basic
* Height: 0.3 meters (0.98 ft)
* Weight: 3.2 kilograms (7.1 lb)
* Gender Distribution: 50% Male
* Ability: Shield Dust
* Type: Bug/Poison
* Species: Hairy Bug/Hairy
* Egg Group: Bug
* Hatch Steps: 3840
* Catch Rate: 255
* Base Experience: 52
* Max Experience: 1000000
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | 40 | 35 | 30 | 50 | 20 | 20 |
| Base Stats (GS/C) | 40 | 35 | 30 | 50 | 20 | 20 |
| Base Stats (RS/FL/E) | 40 | 35 | 30 | 50 | 20 | 20 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | 283 | 168 | 158 | 198 | 138 | 138 |
| Max Stats (GS/C) | 283 | 168 | 158 | 198 | 138 | 138 |
| Max Stats (RS/FL/E) | 284 | 185 | 174 | 218 | 152 | 152 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Moves that deal 200% of their damage to Weedle: fire, flying, rock, psychic Moves that deal 50% of their damage to Weedle: poison, bug, fairy Moves that deal 25% of their damage to Weedle: grass, fighting

## How to Evolve

Weedle evolves at level 7.

## Moveset

| Level | Red / Blue | Yellow | Gold / Silver | Crystal | Ruby / Sapphire Emerald XD / Colosseum | Fire Red / Leaf Green |
| Start | Poison Sting String Shot | Poison Sting String Shot | Poison Sting String Shot | Poison Sting String Shot | Poison Sting String Shot | Poison Sting String Shot |

## Trading Cards

* Base Set #69 - Weedle
* Gym Challenge #82 - Koga's Weedle
* Neo Discovery #70 - Weedle
* Skyridge #114 - Weedle
* Skyridge #115 - Weedle
* EX FireRed & LeafGreen #86 - Weedle
| Basic: Weedle | Stage 1: Kakuna | Stage 2: Beedrill |
# Pokémon/Pokédex/Will-O-Wisp

Will-O-Wisp burns the target, and has a 75% chance to hit. It deals no damage.
# Pokémon/Pokédex/Whiscash
## Basic Statistics

* National Index: 340
* Johto Index: 340
* Hoenn Index: 128
* Stage: Stage 1
* Height: 0.9m/2'11"
* Weight: 23.6kg/52.0lb
* Gender Distribution: 50% Male
* Ability: Oblivious
* Type: Water/Ground
* Species: Whiskers
* Egg Group: Water 2
* Hatch Steps: 5120
* Catch Rate: 75
* Base Experience: 158
* Max Experience: 1000000
* Hold Item in Advance: none
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | - | - | - | - | - | - |
| Base Stats (GS/C) | - | - | - | - | - | - |
| Base Stats (RS/FL/E) | 110 | 78 | 73 | 60 | 76 | 71 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | - | - | - | - | - | - |
| Max Stats (GS/C) | - | - | - | - | - | - |
| Max Stats (RS/FL/E) | 424 | 280 | 269 | 240 | 276 | 265 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are very good on Whiscash: Grass Move types which are bad on Whiscash: Fire, Poison, Rock, Steel Move types which don't effect Whiscash: Electric
All other move types are normal effectiveness on Whiscash.

## Moveset

| Level | Ruby / Sapphire Emerald XD / Colosseum | Fire Red / Leaf Green |
| Start | Tickle Mud-Slap Mud Sport Water Sport | Tickle Mud-Slap Mud Sport Water Sport |
| 6 | Mud-Sport Water Sport | Mud-Sport Water Sport |
| 11 | Water Gun | Water Gun |
| 16 | Magnitude | Magnitude |
| 21 | Amnesia | Amnesia |
| 26 | Rest Snore | Rest Snore |
| 36 | Earthquake | Earthquake |
| 46 | Future Sight | Future Sight |
| 56 | Fissure | Fissure |

### TM/HM

* RS/FL: Attract, Blizzard, Dive, Double Team, Earthquake, Facade, Frustration, Hail, Hidden Power, Hyper Beam, Ice Beam, Protect, Rain Dance, Rest, Return, Rock Smash, Rock Tomb, Sandstorm, Secret Power, Strength, Surf, Toxic, Water Pulse, Waterfall

### Evolution

* RS/FL: Spark, Thrash, Whirlpool

## Trading Cards

* EX Dragon #48 - Whiscash
* EX Deoxys #28 - Whiscash
| Basic: Barboach | Stage 1: Whiscash | (No Stage 2) |
# Pokémon/Pokédex/Wiglett
## Description

A eel-like pokémon.

## Base Statistics

A Water type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Wiglett: grass, electric Moves that deal 50% of their damage to Wiglett: fire, water, ice, steel

## How to Evolve

Evolves to Wugtrio.

## Notes

Introduced in Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Whismur
## Basic Statistics

* National Index: 293
* Johto Index: 293
* Hoenn Index: 45
* Stage: Basic
* Height: 0.6m/2'0"
* Weight: 16.3kg/36.0lb
* Gender Distribution: 50% Male
* Ability: Soundproof
* Type: Normal
* Species: Whisper
* Egg Group: Monster/Ground
* Hatch Steps: 5120
* Catch Rate: 190
* Base Experience: 68
* Max Experience: 1059860
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | - | - | - | - | - | - |
| Base Stats (GS/C) | - | - | - | - | - | - |
| Base Stats (RS/FL/E) | 64 | 51 | 23 | 28 | 51 | 23 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | - | - | - | - | - | - |
| Max Stats (GS/C) | - | - | - | - | - | - |
| Max Stats (RS/FL/E) | 332 | 221 | 159 | 170 | 221 | 159 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are good on Whismur: Fighting Move types which don't effect Whismur: Ghost
All other move types are normal effectiveness on Whismur.

## Moveset

| Level | Ruby / Sapphire | Fire Red / Leaf Green |
| Start | Pound | Pound |
| 5 | Uproar | Uproar |
| 11 | Astonish | Astonish |
| 15 | Howl | Howl |
| 21 | Supersonic | Supersonic |
| 25 | Stomp | Stomp |
| 31 | Screech | Screech |
| 35 | Roar | Roar |
| 41 | Rest Sleep Talk | Rest Sleep Talk |
| 45 | Hyper Voice | Hyper Voice |

### TM/HM

* RS/FL: Attract, Blizzard, Double Team, Facade, Fire Blast, Flamethrower, Frustration, Hidden Power, Ice Beam, Protect, Rain Dance, Rest, Return, Roar, Secret Power, Shadow Ball, Shock Wave, Solarbeam, Sunny Day, Toxic, Water Pulse

### Breeding

* RS/FL: Extrasensory, Smellingsalt, Snore, Swagger, Take Down

## Trading Cards

* EX Hidden Legends #82 - Whismur
| Basic: Whismur | Stage 1: Loudred | Stage 2: Exploud |