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 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.
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.