LMIs in Control/Click here to continue/Robust Controls/H2-Optimal State Feedback Synthesis

Robust H2-Optimal State Feedback Synthesis edit

For systems with uncertain state parameters, a robust controller is needed. H2-optimal control is desirable in minimum-energy applications.

The System edit

The static formulation of the system is given as follows:

 

Where   is the state and   is the input at any  

 ,  ,  , and   are rational matrices with variance  .

The Data edit

The state matrices are defined as:

 ,

 

 

 

The LMI:H2-Optimal State Feedback Synthesis edit

Suppose   . Then the following are equivalent:

1.      for all  .

2.    for some   and   such that   for all  and

 

 

 

for all  

Conclusion: edit

The method above can be used to find an H2-optimal robust state feedback controller for a system with uncertain parameters.

Implementation edit

This implementation requires Yalmip and Sedumi.

H2-Optimal State Feedback Synthesis

Related LMIs edit

Full State Feedback Optimal H_inf LMI

External Links edit


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