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

WIP, Description in progress

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

ProblemEdit

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

 

 

 

TheoremEdit

A discrete-time dynamic output feedback LTI controller with 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   norm of the closed-loop transfer matrix   from the exogenous input   to the performance output   is less than  , where

 

 

 ,

 ,

 ,

 ,

 ,

 ,

and  .

Synthesis MethodEdit

Solve for   and   that minimizes   subjects to  

 

 

 

 

 

tr 

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

External LinksEdit

A list of references documenting and validating the LMI.

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