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
Linear Matrix Inequalities (LMIs) and LMI techniques are powerful design tools in areas ranging from control engineering to system identification and structural design.
- 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.
- LMI Solvers
There is a solver for each of the three generic optimization problems.
- Minimize Linear Objectives under LMI Constraints
Solve an optimization problem using the
- 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
showlmito analyze and validate the results of an LMI optimization.
- Advanced LMI Techniques
LMI Lab supports structured matrix variables, complex-valued LMIs, custom objectives.