LMIs in Control/pages/Full-State Feedback Optimal Control H2 LMI

Full State Feedback Optimal ControlEdit

Full State Feedback in general has the goal of positioning a system's closed loop poles in a desired location. This allows us to specify the performance of the system such as requiring stability or bounding the overshoot of the output. By minimizing the   norm of this system we are minimizing the effect noise has on the system as part of the performance specifications, particularly when there is information about the distribution of the noise.

The SystemEdit

The system is represented using the 9-matrix notation shown below.

 

where   is the state,   is the regulated output,   is the sensed output,   is the exogenous input, and   is the actuator input, at any  .

The DataEdit

 ,  ,  ,  ,  ,  ,  ,  ,   are known.

The LMI: Optimal Output Feedback Control LMIEdit

The following are equivalent.

1) There exists a   such that  

2) There exists  ,   and   such that

 
 
 

where  

Conclusion:Edit

This LMI solves the   optimal full state feedback problem and finds the upper bound of the   norm of the system,  . In addition to this the controller   is also found in the process.

ImplementationEdit

This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/FSF_H2.m

Related LMIsEdit

Full State Feedback Optimal   LMI

External LinksEdit

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