[<< wikibooks] LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Rank Matrix Completion
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LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Low-Rank Matrix Completion

This is a Template for Creating An LMI Page


== The System ==

  
    
      
        
          
            
              
                
                  
                    
                      x
                      ˙
                    
                  
                
                (
                t
                )
              
              
                
                =
                A
                x
                (
                t
                )
              
            
            
              
                x
                (
                0
                )
              
              
                
                =
                
                  x
                  
                    0
                  
                
              
            
          
        
      
    
    {\displaystyle {\begin{aligned}{\dot {x}}(t)&=Ax(t)\\x(0)&=x_{0}\end{aligned}}}
  


== The Data ==
A List of inputs needed for the problem to be well-defined.


== The Optimization Problem ==
A description of the Problem to be solved, if appropriate.


== The LMI: The Lyapunov Inequality ==
Title and mathematical description of the LMI formulation.

  
    
      
        
          
            
              
                
                  Find
                
                
                X
                :
              
              
            
            
              
                
                  
                    [
                    
                      
                        
                          X
                        
                      
                    
                    ]
                  
                
              
              
                
                >
                0
              
            
            
              
                
                  
                    [
                    
                      
                        
                          
                            A
                            
                              T
                            
                          
                          X
                          +
                          X
                          A
                        
                      
                    
                    ]
                  
                
              
              
                
                <
                0
              
            
          
        
      
    
    {\displaystyle {\begin{aligned}{\text{Find}}\;X:&\\{\begin{bmatrix}X\end{bmatrix}}&>0\\{\begin{bmatrix}A^{T}X+XA\end{bmatrix}}&<0\end{aligned}}}
  


== Conclusion: ==
Interpretation of the results of the LMI


== Implementation ==
A link to CodeOcean or other online implementation of the LMI


== Related LMIs ==
Links to other closely-related LMIs


== External Links ==
A list of references documenting and validating the LMI.

LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.


== Return to Main Page: ==