LMIs in Control/pages/LMI for Mixed H2 Hinf Output Feedback Controller

LMI for Mixed Output Feedback Controller

The mixed output feedback control has been known as an example of a multi-objective optimal control problem. In this problem, the control feedback should respond properly to several specifications. In the controller, the channel is used to improve the robustness of the design while the channel guarantees good performance of the system.

The SystemEdit

We consider the following state-space representation for a linear system:

 

where  ,  ,  , and   are the state matrix, input matrix, output matrix, and feedforward matrix, respectively.

These are the system (plant) matrices that can be shown as  .

The DataEdit

We assume that all the four matrices of the plant,  , are given.

The Optimization ProblemEdit

In this problem, we use an LMI to formulate and solve the optimal output-feedback problem to minimize both the <> and <> norms. Giving equal weights to each of the norms, we will have the optimization problem in the following form:

 

The LMI: LMI for mixed /Edit

Mathematical description of the LMI formulation for a mixed  /  optimal output-feedback problem can be written as follows:

 

where   and   are defined as the   and   norm of the system:

 

Moreover,  ,  ,  ,  ,  , and   are variable matrices with appropriate dimensions that are found after solving the LMIs.

Conclusion:Edit

The calculated scalars   and   are the   and   norms of the system, respectively. Thus, the norm of mixed  /  is defined as  . The results for each individual   norm and   norms of the system show that a bigger value of norms are found in comparison with the case they are solved separately.

ImplementationEdit

A link to Matlab codes for this problem in the Github repository:

https://github.com/asalimil/LMI_for_Mixed_H2_Hinf_Output_Feedback_Controller

Related LMIsEdit

External LinksEdit

  • [1] - LMI in Control Systems Analysis, Design and Applications

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