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LMI Solvers

Feasibility, minimization of linear objectives, eigenvalue minimization

Robust Control Toolbox™ LMI functionality serves two purposes:

  • Provide state-of-the-art tools for the LMI-based analysis and design of robust control systems

  • Offer a flexible and user-friendly environment to specify and solve general LMI problems (the LMI Lab)

For users interested in developing their own applications, the LMI Lab provides a general-purpose and fully programmable environment to specify and solve virtually any LMI problem. Note that the scope of this facility is by no means restricted to control-oriented applications.


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lmieditSpecify or display systems of LMIs as MATLAB expressions
setlmisInitialize description of LMI system
lmivarSpecify matrix variables in LMI problem
lmitermSpecify term content of LMIs
newlmiAttach identifying tag to LMIs
getlmisInternal 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
lmiinfoInformation about variables and term content of LMIs
lminbrReturn number of LMIs in LMI system
matnbrNumber of matrix variables in system of LMIs
decnbrTotal number of decision variables in system of LMIs
dec2matGiven values of decision variables, derive corresponding values of matrix variables
mat2decExtract vector of decision variables from matrix variable values
decinfoDescribe how entries of matrix variable X relate to decision variables
feaspCompute solution to given system of LMIs
mincxMinimize linear objective under LMI constraints
defcxHelp specify cTx objectives for mincx solver
gevpGeneralized eigenvalue minimization 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