LMIs in Control/pages/CT-SOFS

LMIs in Control/pages/CT-SOFS

In view of applications, static feedback of the full state is not feasible in general: only a few of the state variables (or a linear combination of them, , called the output) can be actually measured and re-injected into the system.
So, we are led to the notion of static output feedback

The SystemEdit

Consider the continuous-time LTI system, with generalized state-space realization  

 

The DataEdit

  •  
  •  

The Optimization ProblemEdit

This system is static output feedback stabilizable (SOFS) if there exists a matrix F such that the closed-loop system
 
(obtained by replacing   which means applying static output feedback)
is asymptotically stable at the origin

The LMI: LMI for Continuous Time - Static Output Feedback StabilizabilityEdit

The system is static output feedback stabilizable if and only if it satisfies any of the following conditions:

  • There exists a   and  , where  , such that


  


  • There exists a   and  , where  , such that


  


  • There exists a   and  , where  , such that


  


  • There exists a   and  , where  , such that


  


ConclusionEdit

On implementation and optimization of the above LMI using YALMIP and MOSEK (or) SeDuMi we get 2 output matrices one of which is the Symmeteric matrix   (or  ) and  

ImplementationEdit

A link to the Matlab code for a simple implementation of this problem in the Github repository:

https://github.com/yashgvd/LMI_wikibooks

Related LMIsEdit

Discrete time Static Output Feedback Stabilizability
Static Feedback Stabilizability

External LinksEdit

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