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LMI Solvers

Feasibility, minimization of linear objectives, eigenvalue minimization

Functions

getlmisInternal description of LMI system
lmieditSpecify or display systems of LMIs as MATLAB expressions
lmitermSpecify term content of LMIs
lmivarSpecify matrix variables in LMI problem
newlmiAttach identifying tag to LMIs
setlmisInitialize description of LMI system
dellmiRemove LMI from system of LMIs
delmvarRemove one matrix variable from LMI problem
setmvarInstantiate matrix variable and evaluate all LMI terms involving this matrix variable
dec2matGiven values of decision variables, derive corresponding values of matrix variables
decinfoDescribe how entries of matrix variable X relate to decision variables
decnbrTotal number of decision variables in system of LMIs
lmiinfoInformation about variables and term content of LMIs
lminbrReturn number of LMIs in LMI system
mat2decExtract vector of decision variables from matrix variable values
matnbrNumber of matrix variables in system of LMIs
defcxHelp specify cTx objectives for mincx solver
feaspCompute solution to given system of LMIs
gevpGeneralized eigenvalue minimization under LMI constraints
mincxMinimize linear objective under LMI constraints
evallmiGiven particular instance of decision variables, evaluate all variable terms in system of LMIs
showlmiReturn left and right sides of LMI after evaluation of all variable terms

Examples and How To

Specify LMI System at the Command Line

This example shows how to specify LMI systems at the command line using 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.

Modify a System of LMIs

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

Concepts

Linear Matrix Inequalities

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

LMIs and LMI Problems

A linear matrix inequality is a convex constraint.

LMI Applications

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.

Specifying a System of LMIs

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.

LMI Solvers

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.

Validating Results

Use evallmi and showlmi to analyze and validate the results of an LMI optimization.

Advanced LMI Techniques

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

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