LMIs in Control/pages/dt mixed H2 Hinf optimal output feedback control

WIP, Description in progress

This part shows how to design dynamic outpur feedback control in mixed and sense for the continuous time.

Problem

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Consider the discrete-time generalized LTI plant   with minimal state-space realization

 

 

 

Theorem

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A continuous-time dynamic output feedback LTI controllerwith state-space realization   is to be designed to minimize the   norm of the closed-loop transfer matrix   from the exogenous input   to the performance output   while ensuring the H∞ norm of the closed-loop transfer matrix   from the exogenous input   to the performance output   is less than  , where

 

 

 ,

 ,

 ,

 ,

 ,

 ,

and  .


Synthesis Method

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Solve for   and   that minimizes   subjects to  

 ,

 ,

 ,

 

 

tr 

where  .

The controller is recovered by

 

 

 

 , and the matrices   and   satisfy  . If  , then   and  .

Given   and  , the matrices   and   can be found using a matrix decomposition, such as a LU decomposition or a Cholesky decomposition.

If   then it is often simplest to choose   in order to satisfy the equality constraint  .



WIP, additional references to be added

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A list of references documenting and validating the LMI.

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