LMIs in Control/pages/LMI for convex minimization problem
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LMIs in Control/pages/LMI for convex minimization problem
The System
[edit | edit source]Let and are matrix functions of appropriate dimensions.
Moreove, the matrix functions and are linear in vector where is an vector.
The Data
[edit | edit source]A convex function is given and is the vector of decision variables.
The Optimization Problem
[edit | edit source]The optimization problem is to minimize the convex function such that a contraint between two convex functions are satisfied for the decision variables.
The LMI: LMI for convex minimization problem
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Conclusion:
[edit | edit source]Implementation
[edit | edit source]A link to Matlab codes for this problem in the Github repository:
Related LMIs
[edit | edit source]External Links
[edit | edit source]A list of references documenting and validating the LMI.
- [1] - LMI in Control Systems Analysis, Design and Applications