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.
Specify Systems of LMIs
|Specify or display systems of LMIs as MATLAB expressions|
|Initialize description of LMI system|
|Specify matrix variables in LMI problem|
|Specify term content of LMIs|
|Attach identifying tag to LMIs|
|Internal description of LMI system|
|Remove LMI from system of LMIs|
|Remove one matrix variable from LMI problem|
|Instantiate matrix variable and evaluate all LMI terms involving this matrix variable|
|Information about variables and term content of LMIs|
|Return number of LMIs in LMI system|
|Number of matrix variables in system of LMIs|
|Total number of decision variables in system of LMIs|
|Given values of decision variables, derive corresponding values of matrix variables|
|Extract vector of decision variables from matrix variable values|
|Describe how entries of matrix variable X relate to decision variables|
Linear Matrix Inequalities (LMIs) and LMI techniques are powerful design tools in areas ranging from control engineering to system identification and structural design.
Applications of LMIs include robust stability, optimal LQG control, estimation, and many others.
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.
- Specify LMI System at the Command Line
- Specify LMIs with the LMI Editor GUI
- Querying the LMI System Description
- Modify a System of LMIs
There is a solver for each of the three generic optimization problems.
Solve an optimization problem using the
LMI solvers optimize a vector of the free scalar entries of the matrix variables. These entries are called the decision variables.
showlmi to analyze
and validate the results of an LMI optimization.
LMI Lab supports structured matrix variables, complex-valued LMIs, custom objectives.