Feasibility, minimization of linear objectives, eigenvalue
minimization

`getlmis` |
Internal description of LMI system |

`lmiedit` |
Specify or display systems of LMIs as MATLAB expressions |

`lmiterm` |
Specify term content of LMIs |

`lmivar` |
Specify matrix variables in LMI problem |

`newlmi` |
Attach identifying tag to LMIs |

`setlmis` |
Initialize description of LMI system |

`dellmi` |
Remove LMI from system of LMIs |

`delmvar` |
Remove one matrix variable from LMI problem |

`setmvar` |
Instantiate matrix variable and evaluate all LMI terms involving this matrix variable |

`dec2mat` |
Given values of decision variables, derive corresponding values of matrix variables |

`decinfo` |
Describe how entries of matrix variable X relate to decision variables |

`decnbr` |
Total number of decision variables in system of LMIs |

`lmiinfo` |
Information about variables and term content of LMIs |

`lminbr` |
Return number of LMIs in LMI system |

`mat2dec` |
Extract vector of decision variables from matrix variable values |

`matnbr` |
Number of matrix variables in system of LMIs |

**Specify LMI System at the Command Line**

This example shows how to specify LMI systems with the LMI Lab tools.

**Specify LMIs with the LMI Editor GUI**

Use the LMI Editor to specify LMI systems interactively.

**Minimize Linear Objectives under LMI Constraints**

Solve an optimization problem using the `mincx`

solver.

Once specified, you can modify a system of LMIs by deleting an LMI, removing a variable, or fixing a variable's value.

Linear Matrix Inequalities (LMIs) and LMI techniques are powerful design tools in areas ranging from control engineering to system identification and structural design.

A linear matrix inequality is a convex constraint.

Applications of LMIs include robust stability, optimal LQG control, estimation, and many others.

**Tools for Specifying and Solving LMIs**

The LMI Lab blends tools for the specification and manipulation of LMIs with powerful LMI solvers for three generic LMI problems.

To specify a system of LMIs, declare the dimensions and structure of each matrix variable, and then describe the terms of each LMI.

**How lmivar and lmiterm Manage LMI Representation**

The LMI tools create global variables that are not visible in the workspace.

**Querying the LMI System Description**

Extract and display relevant information from the software's representation of an LMI system.

There is a solver for each of the three generic optimization problems.

**Conversion Between Decision and Matrix Variables**

LMI solvers optimize a vector of the free scalar entries of the matrix variables. These entries are called the decision variables.

Use `evallmi`

and `showlmi`

to
analyze and validate the results of an LMI optimization.

LMI Lab supports structured matrix variables, complex-valued LMIs, custom objectives.

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